Don't Pick a Fight
This is one of the fundamental rules here: do not fight unless you need to. Even with proper training, attempting to handle a drunk man with a knife while unarmed is a deadly task.
I'll be answering this from a historic European martial arts perspective, which has a surprising amount of things to say about drunks and street fighting. Until someone pulls a gun, these techniques are highly applicable. Their society was full of people with easy access to knives, clubs, and booze.
So please consider these options. I leave the actual techniques to practice in your local club or dojo; these are fairly applicable with other systems too! Live training is better than any post on the internet will ever be.
The major point here is that fighting is inherently risky. A mistake can mean an incurable condition for you or your opponent. "Incurable conditions" range from a small ache that pesters you forever to immediate death. It's really better (well, less risky) to avoid fights whenever possible.
Drunks Are Dangerous
It has been recognized throughout the ages that a drunk man with a weapon is super dangerous, even more so than a sober man. Why? Because their normal inhibitions and "I-want-to-live" instincts are dulled or entirely muted. Doing an all-out attack that kills both parties seems like a better idea when drunk. Some medieval fencing schools required an armed fight with a drunk to graduate. That's a raw deal!
Grab A Weapon
This levels the playing field a bit more. This opens up parrying, "beating" their weapon away, and maybe even giving them pause before commiting to an attack. The calculus of engagement disfavors assaulting armed opponent over an unarmored one. It requires a certain level of drink or rage to overcome that instinctual inhibition.
Use Your Coat
This is a classic defense against knives and sticks. You can gain some degree of protection from knives and other weapons by wrapping your forearm several times with a coat. Also, kiss that coat goodbye, as it will get ripped and slashed instead of you! Use it to deflect cuts and thrusts, control their weapon, and make your move to get them disarmed and out of the fight.
Use Their Tells
A drunk, unless a well practiced fighter, is going to have some big tells. It comes with inhibited executive function of the brain. Read the windups and shifts of weight: interrupt them and put them on the defensive.
Put Them Down
The general medieval consensus is that you put neutralize enemies as soon as possible. That doesn't always mean killing. Fiore Dei Liberi recommends, especially in a grapple or wrestle, that you break the arms (or other joints) and send them to the ground. Pins, locks, as well as yanks/cranks are all not-inherently-lethal options here.
Advocating for extreme violence off the bat does seem bad, but the fact is that you do not know what the other person is capable of. They could injure or kill you, given the chance. Any leniency shown to your opponent while they are still combat-capable gives them a chance to injure or kill you. This is the primary reason why old masters (and I) advocate to put your opponent out of the fight, and fast. Once again, this doesn't mean kill them, it means remove their ability to fight.
Have Friends
Numbers is a HUGE advantage! If you look at professional bouncers, they do not actually use much combat expertise when applying force. They use numbers. One on one, it can be unclear who would win. Three on one is pretty much guaranteed to have the three walk away alive and mostly unharmed!
