I think some non-undead monsters could easily be utilized. I mean, how are non-undead monsters reacting to this?
A hag or devils could be using this opportunity to snare people. "I'll give you power to avoid/escape/seek vengeance on the undead. It won't cost you... much."
Demons (or other entities) might be attracted to the place, either because they're working for Orcus, or they just want to revel and enjoy the carnage.
Same thing with entities that might feed on entropy (suffering, anguish, terror, etc). They're not exactly causing any more damage, necessarily.
Scavengars (like gnolls) might be attracted to the amount of corpses (like the bodies they're fishing out of the river). They just want easy food.
Something might consider the House/farm-area its territory, and the PCs are on its hunting grounds. Or it could be a little more tyrannical; "You will give me tribute in payment for being on my land."
Cultists of Orcus might be moving into the area. I mean, this is a big event, no doubt, and they might see this as a Sign. The Ashen Covenant (eDragon) wants to overthrow the Raven Queen, and install Orcus as God of the Dead; one faction believes doing this requires converting more people to undead than those who are alive. Those fanatics might see this as the First Step.
A necromancer might be looking to ride in and steal some of the undead for an army. Or investigate some new breeds. He might even hire the PCs to take him into the city, so that he can take notes/look for prime subjects/do research on the Rift. The PCs suddenly playing Zombie Kidnapper, hunting undead, might be an interesting turn of opportunity.
More social monsters might consider this the opportunity to move into a city. Something like a Medusa might move into a fancy mansion, confident she can petrify anything problematic. She might even hire the PCs to clean the mansion out first, look for weak spots where things might get in, fortify the place properly, etc.
Is the rift to Negative Energy plane, or is it just to the Shadowfell? Because if it's the latter, than things that aren't necessarily undead could have been released. Shadar-Kai, who are used to the dead, could have come over. They could be doing various rituals around the city in order to spread the necromantic taint, or perhaps they are intentionally trying to pave the way for something Bigger and Badder coming through.