Well, I don't know if this situation falls under the asked to stay title or not but last week I was asked to stay by my agency because one of my fellow co-workers didn't show up for her shift.
I had already worked 3-11 and my agency BEGGED me to stay until she found someone to fill the shift...yeah right. Staying for 11-7 didn't bug me near as bad as having to count with the stuffy nurse that was waiting to be relieved. we both knew that if I didn't stay SHE would have to.
Needless to say, I did stay for another shift and since I slept over 8 hours the night before

it wasn't all that bad.
I agree though, the more you frequent the same place the more they think they OWN you.
I still wouldn't trade by Agency Job for the world!!
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