I do not know this person personally, but looking at his activity, he has not played in 10 years and is still a member. Is there anyway to check on this?
I'm a little bit confused by your inquiry. It does seem odd that somebody who hasn't been playing for 10 years is still a member - although are you certain they aren't playing? You can check their RuneMetrics profile by hovering your mouse over the "Community" button at the top of the page - then clicking on the RuneMetrics button. Typing their name will show all recent activity.
Could you be a little more specific on what you're asking please? Since this is a community led forum, most of the assistance that you'll gethere will come in the form of providing details that can be found within various support pages from the website.
The checking that can be done by a player is quite limited as a JMod will never pass information on to you about another player.
Look them up in Runemetrics as suggested by Apazos.
If the account has been active in RS3 within the past twelve years, it will show the last 20 events for the account.
If there is no activity, you could try looking them up in the OSRS High Scores though that will only show activity within the past three months.
If you can see that the account remains a member but has no recent activity in either game then, yes, the player is maintaining membership.
They might be logging in from time to time without actually doing any skill training.
They might be one of the lucky few who have won lifetime free membership.
They just might want to maintain membership despite not playing the game anymore.