Resident Evil 3
This begins before RE 2, but finishes after. It follows Jill Valentine escaping Raccoon City during the T-Virus outbreak. She encounters the Biohazard Countermeasure Service, Umbrella's private army sent to counter the outbreak, and the Nemesis - a new mutant sent to kill members of S.T.A.R.S. With help of UBCS soldier Carlos Oliveira, Jill defeats the Nemesis and escapes the city before the government levels it with a nuclear strike.
Links in the chain
The Nemesis parasite extracted from Lisa Trevor was spliced by Umbrella's Paris lab with four Tyrants to produce the Nemesis: a bio-weapon capable of carrying out orders and using weapons.
Barry also showed up to rescue Jill Valentine at the end of Resident Evil 3, just before the nuclear strike hits Raccoon City - but he has since moved his family to Canada in order to be safe.