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_remaining_time doesn't check that endtime > current time and can return a negative number, which would trigger an EINVAL when passed to select (select_select doesn't seem to check for negative double).
Note that a check is performed through _check_timeout but after having called select, so there are at least two possible ways to get this error:
The process blocks a little before calling select for the first time. This can at least happen here:
 if self.stdin and not self._communication_started:
 # Flush stdio buffer. This might block, if the user has
 # been writing to .stdin in an uncontrolled fashion.
 self.stdin.flush()
 if not input:
 self.stdin.close()
There's also a short race window if the endtime deadline expires between the call to _check_timeout and remaining_time.