In short, yes. Battery tenders can catch fire. They are designed to have a very minimal risk of this happening, however, and are considered to be very safe.

Is it safe to leave battery Maintainer on?

So the short answer is 'Yes, you can leave the Battery Tender^® Plus (BT Plus) battery charger connected to a battery even when it is being used to provide power to another appliance.

Can you leave a battery tender on all winter?

Battery Tender (and other intelligent trickle chargers/maintainers) is designed to charge the battery and keep it charged in floating (trickle charge) mode. You can (and most people do) leave it connected to your battery all winter, even for years if you need to.