Yes, oil cooler failed at 5.5 as a student on a night XC, Instructor landed. Being glued to the six pack as student, never saw the oil pressure drop which happened quick, fortunately for us HE did.
the little Lycoming gave us 2000-3000 rpm’s all the way down, no need to pull dipstick as the oil was all over lower half cowl, wings belly etc… Oil sump was dry. I asked the only mechanic on field how long could that engine could run without oil, he said he didn’t know cause we were first to make it back. He had a warm hanger with his P51 and M20J
All goes back to private training and the quality of ur CFI some prefer to pound things in the students over worked brains.
During your patterns in random spots, Ask yourself if I had engine out, could I make the Rnwy if NOT you are too far away.