This paper shows that for sequential sampling without recall from a Dirichlet process, there exists a finite bound beyond which one will cease sampling with probability 1. The result is valid for Dirichlet processes defined on closed bounded intervals of the real line.
"Finite Stopping in Sequential Sampling Without Recall from a Dirichlet Process." Ann. Statist. 14 (1) 275 - 282, March, 1986. https://doi.org/10.1214/aos/1176349855