  We prove the stability conjecture of $\imath$canonical bases, which was
raised by Huanchen Bao and Weiqiang Wang in 2016, for all locally finite types.
To this end, we characterize the trivial module over the $\imath$quantum groups
of such type at $q = \infty$. This result can be seen as a very restrictive
version of the $\imath$crystal base theory for locally finite types.
