Way back before fire was invented and I worked at Nagios, I managed a Nagios system at another company and had to do exactly this.
The solution back then was to write an
expect script that logged in, ran some commands, and returned. Then wrap that in a bash script to run grep/awk/sed/whatever on the output to determine the status code. Not exactly pretty, but I didn't find a plugin written that did what I wanted.
These days I would look into SNMP for the device. There appear to be some OIDs you can use:
All processes:
https://iphostmonitor.com/mib/oids/CISC ... Table.html
Specific process:
https://iphostmonitor.com/mib/oids/CISC ... Entry.html
A list of more can be found here:
https://iphostmonitor.com/mib/CISCO-PROCESS-MIB.html
Some relevant accompanying info:
https://www.cisco.com/c/en/us/support/d ... -snmp.html