In the Republic of Ireland and the United Kingdom, the P45 is the form that a person is handed when leaving a job. The P45 details income for social security purposes. (The two countries' respective P45s are actually different; it's just that the UK and Ireland have very similar administrative processes here.)
Use of the term "P45" depends on context. See the following examples:
to be given your P45 -- to get fired (possibly unceremoniously)
to ask for your P45 -- to quit your job (possibly unceremoniously and/or defiantly)
to be in possession of your P45 -- to be jobless
(The P45 is handed to the employer when starting at the next job.)
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