Green’s Dictionary of Slang

come through v.

[fig. uses of SE; note late 19C US religious jargon come through, to accept conversion]

1. [20C+] of an object, to deliver, to give up.

2. [1900s] (US) to pay one’s debts.

3. [1900s–50s] (US) to confess, to provide information, to speak out.

4. [1910s+] to act as desired, to do what is wanted.

5. [1910s+] to survive, to overcome problems.