This is absolutely correct. If you lose your job, and you find one for less money than you were making, the government will continue to pay you unemployment compensation, but not the full amount. It depends on how much less you are making. Also, up to 99 weeks this can be collected. Technically, one does not have to take a job for less money than they were previously making...which is why people stay on unemployment for as long as they can.
Is this a factor contributing to the “under-employment” phenomena? 10% unemployed, 10% gave up, 10% working part time but could work full time?