She had an IUD. She told me that she always used condoms, although I find that hard to believe, as you say, she has/had a drinking problem. If you asked her if she had been with close to 1,000 guys, she would deny it, all she has admitted is that it is "over 100", and she gets annoyed if I try to get any more specific with the numbers.
However, she told me that she didn't like she spend nights on her own, so I said "does that mean every night you found a guy to hook up with?", she said "no, no, no...... every other night, because I was often hungover in between"!
So I've taken that to mean that every other night she was having casual sex with some guy. They wouldn't have all been new guys because she said she had a long list of guys she could call on to "party" with, but she also said that if guys caught feelings or got too into her, she would ditch them. She said she would swap guys in and out of that list.
She also admitted to posting on Craigslist for guys to hook up with, when she was at a loose end. She actually said she was very good at hiding the extent of her promiscuity and that no one knew how bad she was. She did this by finding guys that had no connection to people from her past or friends and family. Despite that, and living in a big city, she said she still ran would have hooked up with a guy and only later on find out they had some sort of connection to people she knew, so she would immediately ghost them, and move on. So she was in a big city, and had slept with SO MANY random guys that she ran into multiple guys that knew people she knew in a suburb miles away. That's like walking down a random street in a city and running into your neighbour, it's very unlikely. But if you walk down every street in the city and do that every day for years, then it's less unlikely!
She worked in a lot of bars and got hit on a lot, and has hooked up with guys on her work break, in the parking lot.
She had boyfriends in this time, but she admitted that while that slowed her down a bit, it didn't slow her down much.
Putting all that together, for her to have slept with over 1,000 men, she would be averaging 2 new guys a week for over 10 years. And given everything above... it seems like it could be that high.