My hospital bill is almost two years old. Can the collection agency still pursue payments from me? Thanks

It would help to tell us what state you are in, as laws vary. But 3 years is the shortest duration statute of limitations on open-ended accounts. If you signed an agreement when you entered the hospital saying you would pay your bills then it's maybe much longer. In any event 2 years is well within the statute of limitations so yes, they can come after you.

Also even if it was outside the SOL, a collection agency can attempt to collect it for the rest of your life, phone calls, letters and so on.

All the SOL does is stop them from being able to sue you and get a judgement.

Yes they can at only 2 years old the debt has not reached the SOL yet.