Understand that 'give the elbow' refers to ending a relationship or employment, not physical contact. When the company downsized, several employees were given the elbow.
Pro Tip 2/3
Informal Usage
This phrase is informal, so use it casually among friends or in relaxed settings, not in formal writing. She gave her unreliable friend the elbow after being stood up again.
Pro Tip 3/3
Negative Connotation
Using this phrase often implies a negative reason for dismissal or rejection. The director gave the unprepared actor the elbow just before the play.