Rear light with failure warning It is a thing that I noticed even on cars it is missing: when rear lights fail, the driver does not realize it.

In bicycles it is much more worse it happens, as the cyclist's own life is more exposed.

I would like to know if someone knows about the existence of REAR lights for bicycles that give some feedback about their own failure, without the needing of 
the cyclist to lift up from the bicycle.

My thanks in advance.
The problem is that you have to start considering the failure modes of the failure detection system. You're quite likely to end up with a less robust system or a lot of false alarms if you have a system designed to warn you of failure. 

You also have to consider what faults would be detected:


a dead battery? You'd need another power source to feed your warning 
a briefly open contact causing the light to switch off (I've had a proper brand light do this every pothole on a road bike)? Can this be distinguished from a deliberate switching off? 
accidental switching (e.g. bumped by a pannier)? How is that different from switching it off? 
unlikely failure modes like LED burnout? These shouldn't happen in a well-designed system, and I wouldn't trust failure detection in any other system. 
the light falling off? Quite a likely failure mode but an extra fixing would be more reliable and less effort - and your failure warning service could fall off too. 
Damage (which could be things like a failed connection or loss of focussing optics) due to vibration/fatigue/impact. My helmet-mounted rear light has lost an LED to this, and another flickers, so it happens.  With series-connected LEDs (common on e-bike rear lights) or a failure in a common electrical path, you could easily lose the whole output.


So instead we consider a system designed to confirm that the light is on. If the confirmation fails you stop and check. This could be a design or mounting that deliberately directs a little of the light to where you can see it. Simply mounting your rear light on your seat tube and having a silver-coloured pannier rack is an easy solution to this. A light with some front-facing white/yellow lights that shine between your legs would cost battery power but might increase visibility. 

There are big advantages to multiple independent lights:


you're more visible from more angles (and further away if you add lights up high) 
approaching vehicles can get an idea of how fast they're gaining on you (this really needs multiple constant lights to work well) 
they indicate your size better - important if you're wider than a driver might expect (trailer for example) 
and of course the big one here: if one dies you've still got some minimum level of lighting at the back. 


I take this approach with two steady rear lights and a flashing one on my helmet (also with yellow LEDs on the sides). Sometimes I have a third rear light as I have one on the top of my daughter's seat and one on my spare pannier. 

Another consideration is what you'd do if you detected a failure and it wasn't easy to fix at the side of the road, an hour from home, in complete darkness.  With a backup light or two, just ride on.  Of course this does mean you should check your lights at home - this is just a matter of looking at them as you switch them off and not doing it by feel.