Procrustus has explained it well in the bail bondsman’s instance, but more generally speaking, subrogation involves an insurance company (it could be said that surety is a form of insurance, but one which bears little resemblance to normal casualty insurance like on your home or car) taking steps to collect what it paid out on the policyholder’s behalf. It tries to collect from the person who caused the claim in the first place.
Example: You and your neighbour do not get along well. One night, your neighbour gets so fed up with you that he takes a baseball bat to your car, causing $5000 worth of damage to your car–windows, headlights, taillights, you name it, it’s broken. You make a claim on your insurance. Insurance pays you the $5000 in repairs as per your policy contract, then goes after—that is, subrogates against—your neighbour for the $5000 it paid out. That’s pretty much what subrogation is: the insurance company is trying to get paid back by the person who caused the claim to arise in the first place.
In Trump’s case, if Trump skips bail, then Foster’s will pony up $200,000 to the court. Then, Foster’s will subrogate against Trump to regain the money that it paid out on his behalf. This can take many different forms, but it typically boils down to garnishment of salaries and/or bank accounts, or seizure of assets. In Trump’s case, I don’t know what he has that isn’t protected by some sort of corporation, but there would be something. Foster’s would have a staff whose job it is to find out, and lawyers who could make it happen. In some way, shape, or form, Foster’s would squeeze the $200,000 it paid on Trump’s behalf, out of Trump.
Just for fun, I’m thinking, “Mr. Trump, we’ve just seized the ninth hole at your golf course. The property has been severed, and we now hold title to the ninth hole. You are prohibited from playing the ninth hole, as it now belongs to us. If you want it back, a cashier’s cheque in the amount of $200,000 plus legal expenses is necessary.” A silly example, but I hope that it serves to illustrate the extent to which an insurer could go in order to subrogate against the person who caused it to pay a claim.
Does that help?