1261 sums up the UK scenario succinctly, basically do as much as you can without compramising your primary duties to radar traffic.
Even if we're not providing a radar service, we tend to keep an eye on FIS traffic anyway, most of whom are squawking conspicuity, so if someone leaves the frequency without saying goodbye, we can assess their last known position relative to the area we would expect them to change frequency. If they leave the freq' in an area we're not expecting them to, then we'll try and confirm that they are working the next expected unit or ask the destination airfield to let us know that they're OK. It doesnt take up much extra time and reinforces the message to local GA that we do care about them,

, really - we do