One problem related to abs brake fail has been reported for the 2001 Buick Regal. The most recently reported issues are listed below. Please also check out the statistics and reliability analysis of the 2001 Buick Regal based on all problems reported for the 2001 Regal.
On 1997-2004 "w platform" gm autos, including my Regal, the abs sensor design is flawed in that it's wiring is located in an exposed location at the inside bottom of the wheel hub that any road ditritus can impact, causing the track system off dash light to come on and abs braking to fail. I am now on my 6th replacement incident since 2006, when it happened the 1st time. (2 each on the front wheel hubs and 1 on a rear. Do not know at this time which wheel is involved this time,) every time the little sensor wire breaks or gets cut & you can't just fix the wire, it requires a total replacement of the wheel hub and costs nearly $500 a pop. The wire is ridiculously easy to damage just by driving through plow drift in the driveway or hitting small tree branch detritus on the road that bounces off the undercarriage and snags the wire. Most commonly it breaks inside the insulation and intermitently shorts out when it gets wet, (& disappears when it dries out again) causing the abs system to stutter when braking, & making it even more expensive to diagnose before fixing (an extra $129). Since it's a common (& frequent) dangerous safety defect on all "w platform" gm vehicles from '97-'04, I find it curious that the ntsb hasn't ordered gm to find a fix for this long ago.