2001 Prius Steering Failure

I own a 2001 Toyota Prius with 125,000 miles on it with absolutely no issues until recently. Whenever I take a sharp turn for extended period of time such as driving on a 30mph rated interstate exit loop, the Prius power steering fails and I get a big PS failure light on the MFD. Do you know what could be causing this and whether it is a relatively easy fix or not?

The electric steering gear, which is a known problem area, has failed. The fix is to replace the gear which will probably cost around $1,500 plus labor time, at the Toyota dealer.

I usually offer three words when anyone experiences a major repair with their older vehicles.
"trade it in". Most dealers don't keep old trade-ins. They sell them to auctions (dealer auction -> public auctions). If the condition of the trade-ins are good, they may decide to keep them in their used car lot.
If they don't intend to keep them, most likely they don't even test-drive them at all.
People who buy from auctions are fully aware of the risk involved. Therefore, I don't see any ethical issue here. When I traded in my 2001 Odyssey, the guy just look around the van, took down mileage, and gave me his offer. (oh, he also asked me how much other dealer offered me...) I was so shocked that he did not even test-drive it.
(assuming that your Prius is still drivable - good enough to get to the dealerships.)

Guess i'm in the market for a new car. How's trade-in value on 2001 Prius? w/ 125k miles.

KBB says $4500 in good condition. Expect a lot-guy to offer less.

The steering assemblies are available used (<$500), and it is possible for a generalized shop to do the work.

Another option is to call Toyota Customer experience and see if their phone staff is having a great day. It is possible for them to agree to split the cost.