Well, they’ll never be able to go public, much less get any more financing unless they have some idea of how they will earn money.
I’d imagine that they could earn money in the following ways:
Advertising: Lots of people use their service, they’d be able to make at least a bit of money from this. Probably not too much though.
Selling user information: They could sell user preferences/email addresses to record companies. Record companies could then use this information to hawk products to users based on this information.
Selling subscriptions: They’ll announce it’ll now cost 10 bucks a month to use napster. What are you going to do? There is a risk of napster knockoffs like gnutella taking off if they try this, but it could work.
They’ll be bought out by record companies: Record companies, if they are unable to crush napster, will just throw in the towel and buy them. This would be perhaps coupled with the subscription idea. Napster early investers and founders would make boatloads of money and move on. Record companies would move from a product-based revenue stream to a subscription-based stream.
Partnership with record companies: Napster does the subscription thing, but shares a percentage of income with record companies. Record companies agree to stop suing napster.
What do I think will ultimately become of napster? I’d say it’s 60% record companies are successful in crushing napster through lawsuits, putting off the inevitable for a couple more years, but in the end the game will start all over again with gnutella or another knock-off.
40% that record companies buy/partner with napster and realize that they’re now a service company, making their money off subscriptions, direct-email marketing, and a bit of money off advertising.
In any event, free napster with no ads will not last 
Early investors in napster will most likely lose their asses, but in exchange for that risk, they could become incredibly rich if they go the buyout/partnership route.