Create a very simple php file:

<?php
sleep (200);
phpinfo();
 ?>

Create a Zabbix agent item with key:

web.page.get[localhost/sleep.php]

The agent does not timeout as expected:

time zabbix_get -s localhost -k web.page.get[localhost/sleep.php]
zabbix_get [10644]: Timeout while executing operation

real    1m0.011s
user    0m0.003s
sys     0m0.005s

While the agent itself is still busy and waits for a response until it gets it after 200 seconds.
If the web page doesn't answer at all, the agent seems to keep waiting forever and doesn't recover.