We first show by an example that, unlike the domination of hitting distributions, the process with smaller last exit distributions may not be obtainable from the one with bigger last exit distributions by killing and time-change. Then we prove that, under a fairly general condition, the last exit distributions of a transient Hunt process cannot nontrivially dominate those of another transient Hunt process.
Ming Liao. "Domination of Last Exit Distributions." Ann. Probab. 13 (4) 1358 - 1363, November, 1985. https://doi.org/10.1214/aop/1176992818