Can I send some text to the STDIN of an active process running in a screen session?

This answer doesn’t solve the problem, but it’s left here because 30+ people found it useful, otherwise I would have deleted it long time ago.

Write to /proc/*pid of the program*/fd/0. The fd subdirectory contains the descriptors of all the opened files and file descriptor 0 is the standard input (1 is stdout and 2 is stderr).

You can use this to output messages on the tty where a program is running, though it does not allow you to write to the program itself.

Example

Terminal 1:

[ciupicri@hermes ~]$ cat
shows on the tty but bypasses cat

Terminal 2:

[ciupicri@hermes ~]$ pidof cat
7417
[ciupicri@hermes ~]$ echo "shows on the tty but bypasses cat" > /proc/7417/fd/0