Is there any algorithm so it can solve stable marriage problem with incomplete preference lists
I am not completely familiar with the problem, but maybe these couple of papers (or references therein) dealing with stable marriage with partial preferences (of which your setting could perceived as a special case) may be helpful:

https://www.math.unipd.it/~frossi/stc-care5-cr.pdf

https://www.aaai.org/ocs/index.php/IJCAI/IJCAI13/paper/view/6840/6488