Its generally not, depending upon the battery chemistry. Most cell phones use lipo (lithium-polymer) batteries these days, and leaving one of those plugged in is definitely asking for a fire.
The way to do it would be to find a phone that has a NiMH (nickle-metal-hydride) or a Nicad (nickle-cadmium) battery, and hook it up to a trickle charger at C10 rate (one tenth of the "standard" charge rate, which depends upon the milliamp-hour capacity of that specific battery). Two problems with this… finding a usable phone with such a battery, and setting the C10 rate of the charger. The second problem shouldn't be too difficult; you can find trickle chargers that "pulse" the energy input. You plug it in between the phone and the charger, and it causes the charger to send the charging energy into the battery at timed intervals instead of a steady rate. I have left these two types of batteries, in my R/C model airplanes, on trickle charge for over a year with no damage to the battery or its capacity.
Finding a phone with these batteries… well, that will be the trick.
AFAIK, you cannot do this with the newer lipo and li-on (lithium-ion) batteries. The latter are particularly dangerous in that they are quite intolerant of over-charging or -discharging. Remember some years back when folks were having their cell phones blow up in their face? That was li-on batteries.
The lipos are relatively safe, IF you pay attention to their status. They do not do well when discharged below 20% of rated capacity, nor left fully charged over a long period. They will "keep" fully charged, but every time you do you diminish the capacity somewhat, and its a logarithmatic progression; i.e., gets worse.
ANY of these batteries will fry if kept hooked up to a full rate charger once they are "full". The lithium batteries are a real fire/explosion hazard if handled this way; the nicads and NiMH batteries will just die.
You bring up a very valid concern, one that never occurred to me- probably because I have stash guns in strategic locations and plan on handling business myself; calling the cops to clean up the mess afterward, etc.
If I were going to emplace a "stash phone", what I would do is buy a Go Phone and set up a maintenance schedule on my roster of "Shit to Do on a Regular Basis"; IOW, plug the charger in for 24 hours every two weeks or so.
If you have any e-geek friends, setting up a phone with a nicad or NiMH battery and trickle charger would be an interesting and challenging project… and you'd have a "set and forget" system.
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