If that standard input is from the terminal, the process receives a SIGTTIN signal which will cause it to stop and wait for a SIGCONT signal, which the parent foreground process will presumably send after moving that process back into the foreground, giving it control of the terminal. A shell will typically display a "Stopped" message when one of its background child processes stops that way.
$ (read line; echo got $line )&
+ Stopped ( read line; echo got $line )
$ ps l20418
F UID PID PPID PRI NI VSZ RSS WCHAN STAT TTY TIME COMMAND
1 500 20418 20387 20 0 108532 1288 signal T pts/4 0:00 /bin/bash -
( read line; echo got $line )
(Characters typed at the terminal are in green.)