You have no idea, Chefguy.
Ha…plain, vanilla stock holdings are the easy stuff - traded on exchanges, margin requirements, clearinghouses. It kind of makes you a little bit sympathetic to their decision to just change the accounting rules rather than deal with the more complicated stuff. 
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deltasigma, stop taking it so personally. There is differences in opinions. Yours is welcome. But don’t assume that it is the only valid one. Thank you for your input, but please remember you’re not the only person who can give advice.
Rico
ADDITIONAL MODERATOR NOTE:
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Honestly I don’t know why it happened this way, I’ll ask. All I know is, one day he surprised my wife with an actual stock certificate in her name. We didn’t even have a brokerage account at the time
Yeah, the medallion guarantee did take some time…but it was trivial compared to the rewards of converting the gift into a form where it could be converted to money 
I went to a broker (EdwardJones) and they sold the stock for me, for a reasonable fee. It was extremely easy.
Also of course companies can, and do, issue fractions of a share.
This is 100% correct. I’m an officer of a corporation registered in VA and under the laws of the Commonwealth we can issue fractional shares (VA § 13.1-641) or dispose of fractional ownership interests in a few approved ways. Whether or not you actually issue fractional shares is a decision each company makes for itself and obviously are actually governed by the law of corporations for the State in which the company is incorporated.
I’m only familiar with the Virginia Stock Corporation Act, it’s quite possible that all States allow for fractional share issues.
That is not at all the same as saying that in a DRIP if your ownership is represented as a fractional share, that you actually own an issued fractional share. You can own a fractional interest in a company without owning a fractional share.
No, physical certificates have been perpetually issued since at least the 19th century in the United States and has never stopped as a general practice. It’s much less common now, and many major companies have gone to a purely digital form.
Just looking into some of my current holdings, Kellogg still offers paper certificates I can request.
It is becoming much more rare, I know several major companies did away with issuing physical certificates in the past few years and many of the most notable recent IPO companies will never issue paper certificates. There’s actually a community of individuals who collect paper stock certificates (I’m not one of them, but it might be nice to get one’s hands on one at some point since they will become akin to telegrams and such here soon.) For individuals just looking to collect them you can buy old certificates from eBay from a huge number of companies. Many of them things like early 20th century mining ventures long since bankrupt (so you’re solely buying for the cosmetic/collector’s value.)
I have a fractional share of the moon, but I don’t know which broker it is with.
Rucksinator, you’re probably best off contacting a few brokers and getting quotes. As said above $2/share is ridiculous, but if the fees amount to more than 20% of the value of the stock I’d hold onto them, if possible, as a long term play. If you need the cash then, by all means, sell.
I am actually one of these. I have my brokerage done up in antiques and have mostly old but some current certificates on the walls for display. That and my large portrait of Scrooge McDuck standing atop a pile of gold coins.
Rucksinator, congrats on doing the right thing. For reasons of my own I couldn’t give you that advice, but I’m glad you did it.
As an aside, I am finding Computershare to be extremely incompetent. They ran the sharesave scheme at the company I work for, and trying to get the vested shares transferred into a different holding account has been a long, drawn-out process. This week, after almost two months, they have finally done it… but they’ve screwed up the numbers and types of shares. 
What I meant was, issuing paper certificates as a matter of course. I don’t think that’s been done for decades. I’m happy to admit I’m wrong about that but I don’t think I am. Moving paper around is grossly inefficient compared to electronic transfers and places like DTC IIRC moved very quickly to electronic format once that was an option.
In theory. In practice I could probably have sailed across the Atlantic to the NYSE, picked up the share certificates and swum back to London with them in a ziploc bag in the time it has taken to sort out my share transfer online. :rolleyes:
You can always write to your Congressman. 
I’d agree with that. The last time I held a paper stock certificate as part of my actual investing activity was in the 80s, the last time I think I held one at all was when we were going through a relative’s house to help my cousin with my great aunt’s (her mother’s) estate. We found some stock certificates in drawers and such that they’d had for years [no, none of them were worth millions–they were all blue chip stocks from the 80s so were not worthless either, but none were serious growth stocks so the cousin liquidated all of them for some amount in the low five figures. It’s unfortunate her parents had been allowed to continue managing their finances after entering dementia as they had a decent amount of total assets but ended up with large debts and unpaid bills that wiped out most of the estate’s value.]
Thanks for all of the replies. They reminded me of why I didn’t bother with these in the first place (and I didn’t have any idea how complicated it could be.) These stocks were issued to me as part of my compensation program, part that I didn’t really pay attention to. After I was laid off I thought I had divested myself of everything Lexmark related (including the 401K [I was desperate for money.]) Then I started getting mail about my (almost) 20 shares, and then the occasional dividend check. ($6!! Whoo Hoo!!)
Now, after spending the summer working on getting my house ready to sell instead of working for income, I find myself in need of cash. So I found one of those offer letters and tried to do it. Until I wrote the OP, I hadn’t bothered to read the back about the $2.25 per share. They made it sound like they were doing me a favor: “… we realize that the inconvenience and cost of brokerage commissions may have deterred you from selling or purchasing fewer than 100 shares in the past…”
[Bolding mine]
The first 25 replies made me scared and afraid. So I was happy to see this:
Another issue: The only evidence that I have that I own this is a couple of the check stubs from the dividend checks and the letter offering this “deal” to me from last year. Will this be enough to prove that I own them? Are they going to send me on a hunt for some paper that I theoretically had in my possession 10 years ago?
If you got the letter last year, then it’s probably still with whatever entity manages the compensation program through which you bought the shares and therefore probably isn’t abandoned property. As has been pointed out already, that’s probably going to be an institution like a bank or brokerage but it could also be Computershare. The later might know who the former happens to be and even if they don’t, they might be able to give you good contact info for someone at Lexmark who can tell you. Of course you can also start with Lexmark if you have some idea what dept. that would be.
Once you find out who’s holding the shares for you, they can tell you what their procedures are for claiming them, selling them, etc. It shouldn’t be anywhere near that expensive to sell the shares. I think I pay $10 per trade with my broker. I would expect you to pay a bit more than that but not a lot and certainly not something ridiculous like a per share charge that ends up being a 10% commission. They’re brokers not an escort service.
They’ll need more, but they’ll guide you through it. I believe all I had at the time were my dividend checks, which came quarterly with a statement.
This is the kind of stuff your broker will handhold you through.