Fetching details from the dictionary...

to fail (in getting a job); to miss out (at fishing, hunting, etc.)
to be left out; to be crowded out
「溢れる」 has other readings with different meanings.
就職にあぶれてしまった。
I failed to get a job.
席から溢れる人が出た。
Some people were left without seats.
仕事にあぶれた人が多い。
Many people missed out on jobs.