The bottom line is that if you are using a buyer's agent, the agent makes the offer on your behalf, so if you want to offer let's say, $1.00 for a $1M property, you totally can.
The bigger question is why would you?
There's a low offer, and then there's the possibly offensive offer. If you have a good agent, s/he should be able to guide you through what's potentially reasonable. There may be situations where you'd offer a massively lowball offer and win it, simply because the planets align properly. A friend of mine had won a very low offer simply because of lack of staging, desperation of buyer, extremely rainy day, and a terrible listing agent.
However, it's much more likely that you'll burn through your agent, and several other agents, and then develop a stigma that you're not very serious, experienced, and a time waster. And then no one will want to work with you, except the really bad, desperate agents, because they won't know better. Or they are just really bad, or really desperate.
There are fire sales, for sure. But as many others mentioned here, do some research to see if it's warranted if you want to be successful.
Your agent should be running a couple of CMAs for you so you get a sense of offer needed to win.
As for offering below MLS aka asking price, it's the asking price. Similar to the car dealer, it's MSRP - depending on the market, you may pay over or under to win. In the Bay Area, we're still at the paying over stage, even in Q4. Detroit, you've got a different scenario.