It is shown that under GCH every poset preserves its cofinality in any cofinality preserving extension. On the other hand, starting with ω measurable cardinals, a model with a partial ordered set which can change its cofinality in a cofinality preserving extension is constructed.
"On changing cofinality of partially ordered sets." J. Symbolic Logic 75 (2) 641 - 660, June 2010. https://doi.org/10.2178/jsl/1268917497