Phone charging Lipo battery power bank with 5V regulator overnight charging deep discharge
Take a look at TP4056 modules with battery protection. Julian Ilett has a nice demo on YouTube. I find they work a lot better than more expensive offerings. It certainly protects against deep discharge and cuts off at about 2.8-V and will resume output when the Lipo recovers to about 2.9-V
Power banks (commercial) for phone charging a complex beasts and do more than supply 5.1-V.
The Belkin Pocket Power bank I use, will only supply to a load when the load pulls more than 100-mA.
When the load goes below that, the output shuts down. However, the Belkin supplies output for about 17-minuts after the cut-off load current applies. I kept a power bank running for days supplying an XBee radio by getting the XBee to load 100-mA every 5-minutes, i.e. retriggering the shutdown timer.
In theory, it should have run for about 2-years, but in practice it only ran for two weeks.
I suspect that the Belkin has some power hungry internal circuitry that doesn't show in the load circuit