I don’t work in web development (and didn’t then, either), so this may vary from what others are saying. What I experienced was that there was a downturn in 2001. I was working for myself and had a contract with a Fortune 50 company. They kept us on for about 6 more months after 9/11, then let all of the contractors go. But I had other irons in the fire, so it was fine for a while.
It really hit hard about 2 years later in 2003, when all non-web contract work dried up and clients started having trouble paying for work you’d already done. That was really brutal for me, personally. I was also selling some software in addition to doing the contracting. I got really lucky and someone saw my products and wanted to license them for their particular niche. I was just barely able to hang on until a year later when things mostly returned to normal.
If it hadn’t worked out, I probably could have taken a job doing some development work I hated if I really had to. There were still openings, but they were at places like Accenture, or whatever a small-time version of them would be.