In the classic era, right up into the 1990's, the typical process was that the detouring railroad furnished train crews, and the hosting railroad furnished a pilot. It is still done that way if an Amtrak train detours off of its regular route. Historically, passenger trains would get two home road crews before entering the detour route, and they would alternate working and resting if the detour was long. I knew a Santa Fe Los Angeles Division passenger Engineer whose regular assignment was LA-Barstow, and, in the early 1960's, his crew and another LA Santa Fe crew worked and rested a detour from LA to Kansas City through Nevada, Utah, Wyoming, Colorado and Kansas via UPRR under the guidance of UPRR pilots.
Subsequent FRA requirements for route familiarization and merger-driven haulage agreements have resulted in the older process being followed some of the time with occasional operation of the detouring train by host road crews, though this is not the norm. Today, most host railroads would not have extra crews available much of the time.
A Santa Fe Rules Examiner another Santa Fe Road Foreman of Engines and I were sent to Muscatine, Iowa in 1993, to become qualified between Muscatine and Kansas City, so that we could pilot and qualify Santa Fe crews on detours. This line consisted of part ex-Rock Island and part ex-Milwaukee Road, and was, at that time, operated by Canadian Pacific. It was not a high density railroad, although it had block signals for most of the way and maximum speeds of 50-60 MPH. After hours and hours of waiting, they finally ran a train, and we both rode it. The track was surprisingly good, the CP crew was friendly, and the Milwaukee Road portion had a quaint and ancient CTC system with relay houses constructed of wood framing and asbestos shingle siding. We never made it to Kansas City because of long waits for meets. In fact we never made it to the old joint CRI&P/MILW joint track that was part of the spine line. We sat for hours waiting for a van to rescue us. By the time we arrived in Kansas City by van, the Santa Fe had managed to get enough trains moving that they decided to eliminate Muscatine to KC as a detour route. I slept for 16 hours and let somebody else worry about detours for a while.