How unsafe is to share parts of a password
If I know your password is k bits long and I know the m bits, then I have to brute force the rest of the k-m bits. That's the standard for any algorithm and independent of whether this is prefix, suffix etc. This means that I have $2^{k-m}$ tests to make. 

However, you can even do better, You can say that you have a decayed version of the key, or you have partial key exposure, you have some plaintexts and the according ciphertexts. In this scenario, there are several effective attacks, even for AES, with different approaches, even SAT solvers. Have a look at the following papers:


Halderman, J. Alex, et al. "Lest we remember: cold-boot attacks on encryption keys." Communications of the ACM 52.5 (2009): 91-98. 
Kamal, Abdel Alim, and Amr M. Youssef. "Applications of SAT solvers to AES key recovery from decayed key schedule images." Emerging Security Information Systems and Technologies (SECURWARE), 2010 Fourth International Conference on. IEEE, 2010.
Liao, Xiaojuan, et al. "Using MaxSAT to Correct Errors in AES Key Schedule Images." Tools with Artificial Intelligence (ICTAI), 2013 IEEE 25th International Conference on. IEEE, 2013.


Of course there are limitations as you can see from the papers, but depending on how much bits you want to crack, it might be easier to go this way than brute force them.