If that witness is no longer a viable witness and there is no physical evidence to corroborate the charges then the prosecutor should no longer try that case. They don't have a solid case. The jury should also find the defendant innocent given there wouldn't be any evidence to support charges outside of a single witness.
I have no stats to back this up but I don't think many prosecutors could win cases if the only evidence they had is a single witness. If they had nothing else that would be an EXTREMELY hard case to win.
It also all depends on what you mean by "protect people". If new technology comes about that tests DNA with less DNA available, and that proves a rape from 20 years ago happened, but the statute has run out, who is being protected there? That's a real thing that happens considering when DNA came out the statute had run out on several cases, but that evidence isn't a witness. It's scientific, physical evidence.