The Burlington - NYC run through agreement between Chicago and the Twin Cities that started about 1960 is still in effect. It carried through the Conrail / BN era into NS / BNSF today. CB&Q used an in-cab signal system, so one of their engines always had to lead the NYC engines.
Back to the OP's question...there were instances where a railroad would lease engines from another railroad in the steam or transition era, but it was generally long term, not like for a few hours or days here or there. For example, for several years in the 1950's the Rock Island leased engines from the New York Central in the fall / early winter to help with the grain rush in the Midwest. The situation we see today, with many run-through agreements and power-sharing agreements that make it common to see engines wandering far away from their home tracks really didn't exist until the 1960's. More likely, when a train hit the yard at the end of it's line, the engine would be cut off and serviced, and any cars moving on to a different railroad would be moved to the other road as part of a transfer between the two railroad's yards.
