The effects, and consequences, for the operation, and you, depend on the operation/company concerned.
Short-haul Lo Co Europe (yep, blue & yellow) I always tried to do it (consult), however, I knew the bullsh1t associated with an unscheduled nightstop, and found that even more tiring than just doing 1 more sector to get home (no transport booked, no transport paid for, no hotel booked, no hotel paid for, no nightstop kit/shirt- my fault of course- etc etc) However, I always asked, is everyone OK with this ? & added, if not, feel free to speak to Ops & explain your situation, however, that is YOUR decision, & I advise you ,just be aware of who you work for,& how well they will take this news.
Not undue pressure/influence, but some more "junior" crewmembers were (for their own sakes, not mine , I didn't really care) better offered an honest assessment of their future career prospects with their current employer, before they got too carried away.
I doubt if Air 0'Leary was in the minority in NOT wishing to hear news like this.
Lets be honest here guys, unless you are seriously out of it, is it really worth the hassle ? & if you REALLY are, you are too tired to care, so you will live with it.
Maybe it is way, way, different in Big Airways/Lufthansa/wherever, but most of us poor sods living/operating in the "real world" will, rightly or wrongly, try to keep the show on the road, influenced in no small way by the anticipated grief of the "unscheduled night-stop arrangements"
& the (lightly concealed) repercussions, Crewing can be REALLY awful in some companies.
Get real.