Two problems related to power steering pump have been reported for the 1999 Toyota Corolla. The most recently reported issues are listed below.
Sudden loss of power steering assist due to defective power steering pump pulley. Inner spline on power steering pump pulley stripped out after 49,000 miles, allowing relative motion between the pulley and pump shaft. Resultant pulley wobble allows the serpentine belt to walk off the power steering pump pulley.
Power steering pump is very noisy, like it has no fluid in it. Afraid it may fail soon. Dealer has been notified.