Cells in devices that you do not wish to be a flaming ruin MUST have protection.
Having protection circuits does not guarantee it will not happen.
Cells without protection are intended for use by either manufacturers or experts or enthusiasts who add their own or for suckers.
Whole device protection and cell protection are complementary and serve overlapping but different roles.
4,000 mAh 18650 LiIon batteries are ~~~= 99.9% +0.1% - 0.0% sure to be rubbish.
ie not just < 4000 mAh but << 4000 mAh and low quality.
The people who bogus label cells
Real world experience shows that the value of 'almost' is very high in both cases.
Higher capacity cells can usually be fitted OK.
MUCH higher capacity will lead to long CC tails and overcharge but not an issue here as mAh_new is < to << 4000 mAh.
ADDED:
Notice that in this ad and all their other ads they ALWAYS show non-brand-label views of the battery.
However, you may find that the racing stripes and general colour scheme a good match for the well known "Ultrafire" brand batteries. This may in fact be a real brand and these may be real examples of it BUT you can buy empty shrink wrappers to apply to the battery of your choice with this (or other) branding on it , so caveat emptor. Better nullius emptor I'd hazard.
These ones are a stunning 6800 mAh - a steal at the price. Available here
You'll find others similarly arrayed here and
here - 3000 mAh and 4000 mAh and
and unspecified but with GENUINE CREE 2000 lumen {so 20+ Watt} flashlight for $9.27 and
only 4000 mAh and
that's better - 4200 mAh
and .............
Flee!
Storing them "discharged" to ~3V with the device they were used in
still preserves lots of energy in the battery.
At 3V a Li-ion battery has almost no capacity left.
In this graph two 800mAh batteries were discharged at various rates. At 0.1A there was virtually no capacity left at 3.0V. Even at 1A they were 99% discharged.
Best Answer
While there are certainly design and maintenance practices that can help to prevent or slow degradation, there's not really any practical way to repair degradation that has already happened to a given cell.
However, often a battery is made from multiple cells. And it's often practical to find out which of those are the weakest in terms of reduced capacity and higher internal resistance. If they're in series, the weakest cell will determine the effective capacity of the whole pack. So you can replace just the weak cells to rejuvenate the battery as a whole. Or, since typically the cells are much cheaper than the pack as a whole, just replace all of them.
Be careful, this can be quite hazardous - be sure to research how to do it safely before attempting!