at the old 911 job, absolutely nothing. you have a 12 hour shift, and you are expected to answer every job from start of shift to end. You are not permitted to delay a job for shift change (written policy). units are assigned 1 truck for both day and night, so if they get hit with back to back to back jobs, they might get out 2 hours late, and the relief crew is chilling in quarters.
If you are in quarters, and the night crew is there, they can take the job, but if you are at the hospital and you get a job, than it's all yours, and you will be late.
At new 911 job, almost nothing. 12 hour power trucks can be given jobs up until their end of shift. 24 hour trucks (which also work 12 hr shifts) are treated the same way, but we try to get them back to station so the night crews can go in service. If your truck is a 24 hr, and the next shift is using your truck, then dispatch will try to get you back to quarters, but if they have life threatening calls holding, they might be a while.
Not for nothing, but if you work in a 911 system, don't expect to get out on time. If a calls comes in 5 minutes before your shift ends, oh well, that's the nature of the job. I have been stuck on jobs after my shift ended.
The only time it annoyed me was when my shift ended at 6pm, and we were at the hospital, and at 6:10pm we were sent to another town that we are contracted not to go to (since our town was contracted from 6a to 6p, dispatch said it was ok since our contract was over). that annoyed me, but oh well, it happens.
One agency I am aware of has a written policy that if your shift if 6a to 6pm than you were required to go on any calls up until 6pm. even if your relief was in quarters. apparently they have problems with some people coming in early and others not so, so management made a decree.
IFT is a little different, because it's a SCHEDULING issue. the dispatcher/scheduler needs to take into account crew shifts. again, emergency IFTs and emergency SCTU jobs aside, the person who schedules the runs shouldn't intentionally make you get out late. yes, stuff happens, people get delayed, but that's it. I used to dispatch IFTs, on the afternoon shift, and the morning guy would always leave me with a mess (4 runs scheduled within 15 minutes of each other, yes we only have 3 trucks available). crews would get pissed at me, but I had the mess dropped in my lap, I didn't cause it. a few discussions between me and the Assistant Director fixed the problem, and the morning person no long dispatches.
One thing I want to point out: if your base is located 30 minutes or an hour from where your coverage area is, don't expect to get 0 runs while you are on your way back. you are contracted for 12 hours (or however long your shifts are) to do a job, and while most dispatchers aren't looking to make you get out late, the job needs to get done.