How can I stop an Adult trike when both front brakes fail?
Answering for completeness:

Don't get in this situation and Prevention is better than cure

You should have picked up that the brakes were not as good as they were by feel (poor braking) or on visual inspection noticed that the inner cables were starting to fray.

Most bikes have two independent brakes.  For yours to both fail at the same time is quite unlikely.

And even if you did successfully add a rear brake, a continuous lack of maintenance may leave that in as bad a state as the other two brakes,

A basic M check should be done weekly.