Is there such a thing as a fail-safe, low-power relay?
Fail safes usually include redundant devices configured properly. For instance if you absolutely have to shut off something, this would be two switches in series, so that if one failed to open, the other could have a chance.
Welding shut can happen if a relay is used outside its specification. For AC applications there are some circuits that only open the relays when the current goes through zero, to reduce the chance of arcs. (zero crossing switching). 100 W really is low power though, so the chances of things like this happening with properly made circuits is really low. There is also the practice of arc-suppression circuits, which is a RC circuit connected to the relay contacts.
If you want very low current, then I would not use a mechanical relay.
triac circuits come to mind. Or MOSFETs for lowest current requirement of the controlling circuit. I don't really get why you want to save on the milli-amps when you're using several amps on the heater though...
100W can for example be 8.33 A @ 12 V .. Not too much for a big mosfet with a heat-sink.
Simplest route is a relay. Use two in series if you're concerned about reliability. look up the proper way to shunt back-emf and how to have low 'keep-on' currents.
NOW most relays are rated at a certain number of operations. from a few thousand to hundreds of thousands. So this might be an issue if you will be switching at a high rate, or over many years.
Use a zero-crossing detector to gate the switching signal (just the simple rectifier based circuit) if on AC.
Most reliable timing circuit that will always 'go low' is of course just a RC timing constant. It will not be accurate, but it will never fail to reach a value that is logical 0. Just to stay super safe, there should be a logical OR between TWO RC timing circuits ;) or a majority voter between three RC timing circuits ;) ;) ;) There is quite many things you can do to get theoretically better 'safety'.
Of course it is all up to you how big safety factor you need. But if lives are at stake, you really should be looking for people who did this before, and talk to them.