The word is "eavesdropping."
The word overhearing can have the synonym "eavesdropping," except that it almost always implies intentional overhearing, such as in snooping. Overhearing can mean to become aware of, or (slang) to get wind of.
The word "stealthily" is an adverb. It describes how an action is performed, in a secretive or cautious manner.
I entered the room stealthily, hoping to remain unnoticed.
He stealthily snuck into the clock tower known as Big Ben
sneak
Stealthy , stealthily ,ninja
The sniper crept stealthily through the bushes, trying to remain unnoticed.
Here's an example:The thieves sneaked stealthily through the household, savoring the prospect of some 'well-deserved' money.Hope it isn't too soppy for you...
If by secretly you meant cautiously then walking stealthily or tip toeing .
overhearing
Ignore?
She stealthily approaches the cake cupboard."I will move very stealthily," said the would-have-been diamond thief, seconds before he tripped a laser-triggered alarm.The Royal Commandos stealthily kidnap their target for interrogation.