Messing with a faction/company/whatever too many times will result in them sending hit squads with members/hired mercenary's to go and deal with you. This can happen from killing leaders or taking out important buildings or just plain making them mad, and such like that.
Usually sending an armed groups to patrol around an area looking for you. But there could be other types of encounters, like drive-by by gangsters, soldiers could air drop in via plane, they can wait for you to enter a Pacific town or building before swarming in. Waiting outside your house for a time to strike.
Setting up traps like car bombs, or trash can bombs. They might even get desperate and do something crazy like taking out the power to the city before making an assault.
Maybe they'll try and mess up your missions. Defending targets or stealing away the sought after item and driving away leading to a chase.
You could lay low and wait them out, maybe find a way to make amends with that angered group....
Or you can fight, making them more and more angry and have them waste so many resources trying to deal with you they just give up. Having them be away till they recover.
Might not work with more rich groups like soldiers or the government agencies.