Is it possible to hook up sub woofers in a 2001 Monte Carlo SS with a stock head unit?

You need to use a line out converter, that splices into the rear speaker wires, run rca wires from the LOC to the amp, speaker wire from amp to sub enclosure, speaker wire from sub enclosure to the sub voice coils. Power wire ran to the battery and fused between 6 and 10 inches from battery positive post, ground wire from amp to chassis ground, remote turn on wire (this you can use a fuse tap from radio shack, use a fuse that has power when key is in acc and engine on position, like the windshield wipers).

Yes its completely doable. It might not sound as good as replacing the head unit with an aftermarket deck but it will generally work just fine.

First if your stock HU does not have RCA outs (rarely do they) you with need a line output converter. It basically converts the signal from the factory speakers to an RCA source that you can connect to an amp. Most people will connect these units to the rear speakers so that they don't have to run RCA cables the length of the car.

Here is a bunch of the line output converters. You can find them just about anywhere

http://www.crutchfield.com/S-qxIKOrRnEQb/g_721/Lin...

If you already have that and I will move onto your next problem of the amp not staying on. This could be caused by a few different things. First check that your power cable is connected properly (the connection is tight and clean, the cable itself is not cracked split etc..) and check that it is connected to the amp securely. Next check that your ground cable is sufficient. It also needs to be clean and connected to a stable ground source. If your just going to the body of the car it can cause issues. Try connecting it directly to the frame in the trunk through the spare tire bay (if the spare is located in the trunk) You also need to make sure that the amp turn on wire is connected to stable switched 12V source. Most after market decks have an amp turn on wire included but because you are using the stock HU you will have to find a switched source such as a cigarette outlet or something else that comes on when the key is turned on. It is best to only have the amp on when the radio is on though, some people say it is hard for amps to be turned on all of the time so if you can find the power wire to the radio that may work as well just be careful. If not you can always use a switch to shut the amp off when the radio is off.

Anyway to sum all of that up. Just make sure all of your connections are good, usually a ground problem or the amp turn on wire connection will cause the issue you are having, atleast those are the issues I have ran into while doing this. Anyway hope that helps good luck

Is your Monte Carlo equipped with a Bose audio equipment? if so, you will not want to connect your LOC at the back of the pinnacle unit. you would be greater effective off tapping into the rear speaker wiring interior the trunk.