Systemd socket activation: kill bash script when closing socket

Assuming a minimal example like in [this question](/questions/454731), except for another shell script. systemfoo@.service:

[Unit]
Description=Foo Service
After=network.target systemfoo.socket
Requires=systemfoo.socket

[Service]
Type=oneshot
ExecStart=/bin/bash /opt/foo/foo.sh
TimeoutStopSec=5

[Install]
WantedBy=multi-user.target

systemfoo.socket

[Unit]
Description=Foo Socket
PartOf=systemfoo@.service

[Socket]
ListenStream=127.0.0.1:7780
Accept=Yes

[Install]
WantedBy=sockets.target

/opt/foo/foo.sh

#!/bin/bash

while true; do
    logger -t FOO "Connection received: $REMOTE_ADDR $REMOTE_PORT"
done

When I connect via

nc 127.0.0.1 7780

the script is invoked correctly. But when I quit nc with CTRL-C, the script runs forever. Is there a mechanism to send a SIGTERM to the script process, when closing the socket (I assume nc does that when quitting)?