From what I can see from the picture, the tree seems fairly small and wouldn’t necessarily do much damage in the event of a failure. If they want to keep it suggest heavy reduction pruning and make it as safe as possible for them.
Oddly enough, many people have emotional connections with their trees. You just never know how a client may be connected to a tree and I often will ask. On one occasion, there was a large Maple in the backyard posing serious threats to the house and the patio where the client spent a lot of time. When they insisted on keeping the tree I asked, “I’m curious why you love this tree so much, would you mind sharing?” They then proceeded to tell me about their kids and how they would swing on a rope swing from the tree and how they used to climb it all the time. They felt like if they lost their tree they would lose a connection with their kids. We heavily reduced the outer crown, installed some cabling and left it for them to enjoy.