Question: Is it possible to have a Mahlo cardinal $\kappa$ such that there is a $\kappa$.c.c. forcing that makes it non-Mahlo?
If this is possible then this forcing must change the cofinality of all but non stationary many inaccessible cardinals below $\kappa$, so at least large cardinals in the region of measurable cardinals of large Mitchell order seem to be unavoidable.
In order to avoid trivialities (such as $Add(\omega,\kappa), Col(\omega, <\kappa)$ ) I require, as Mohhamad suggested, that the forcing preserves the inaccessiblity of $\kappa$.
I'm also interested in the cases where the forcing make $\kappa$ weakly inaccessible, but still destroy its weak Mahloness.