After how low a battery discharged it can be brought back to life using a
1.typical charger
2.Any method possible(Mention the method)

 

There is no hard and fast rule. Lead acid are less forgiving than most. Reverse voltage of half a volt, caused by batteries being in series, will kill many types of rechargeable batteries.

 

Presumably your 3.7V battery (cell) is a lithium type? If so it needs a special charging/discharging regime to avoid the risk of fire/explosion.
Have a look at this for info.

 

General purpose Lithium Ion battery charger protection circuits usually cut off the discharge when the voltage drops to 3 volts. The chargers will not recharge a battery if the voltage drops much below this voltage. If the voltage drops below 2.7 volts, the cell will be damaged and will no longer hold a charge. If the voltage drops to below 3 volts but above 2.7 volts, the cell can usually be recovered by applying a current controlled power supply directly across the output terminals until the voltage increases to above the charger cut off voltage. Then the cell can be recharged normally.
The figures I quoted are typical. If you are working with a battery from a specific manufacturer, you should check the data sheet for the actual values.

 

I've seen some videos in youtube using a method called "bump charging" Is this possible? Are there there any disadvantages or long-term problems other than safety? Will this recovered li-ion battery function as normal afterwards? Why regular chargers stop charging if dropout voltage get lower than 3v(Any safety concerns)?

Reviving a battery with 0.3v -

Reviving a battery with 0.5v -

 

Batteryuniversity.com and most Lithium battery charger IC datasheets say that a Lithium battery cell that is discharged too low is ruined.
They say when the voltage is too low then the Lithium ions have turned into dangerous explosive and flammable metallic Lithium.
Most Lithium battery charger ICs attempt to charge at a low current when a low voltage is detected and if the voltage does not rise then it stops and gives an error message.

 

In other words, a Lithium battery that has been over-discharged and then forced to take a recharge becomes a serious fire hazard.

 

I use an OPUS BT-C3100 charger for AA and AAA cells. The charger is multi-chemistry.

3.7 V lithium packs can be made with cells in parallel. They could be a problem.
Lithium packs a multiple of 3.7V would use a Balance Charger. The charger has access to all of the cells and can equalize the cell voltages.

See http://img.banggood.com/images/upload/2014/04/Powerfocus BT-C3100 OPERATING INSTRUCTIONS.pdf

 

In other words, a Lithium battery that has been over-discharged and then forced to take a recharge becomes a serious fire hazard.

No! As I explained above, If the voltage has dropped to below the cut off level of the charger, but is still above 2.7 volts, it is quite safe to charge it from an external source. The usual charge rate is 37% of the current stated in the ampere hour capacity of the battery. If the voltage has dropped to below the recovery level, it will simply not take a charge.
It becomes dangerous when a cell is charged at a higher current or to a higher voltage than is recommended, or if the cell is physically damaged. Then the temperature can rise and may get to a point where the cell will ignite and explode.

 

Re-read post #6 above, and the link to BatteryUniversity in post #3. A lithium battery excessively discharged changes internal chemistry, which makes it less stable. *THAT* is why a charger will not charge if the terminal voltage is too low.

 

Less stable means that it is ready to explode and/or catch on fire.