Open source software is safe to modify.

Depending on the open source license used by a software, it may or may not be necessary to release the source code of the modified to your users.

In the case of GPL, any changes that you make still belongs to you and you can prevent other people from using the portion that you have created as long as you don't distribute the modified program. If you do distribute the modified program, you are bound by the gpl to make available the source code to people who uses your software.

BSD license is even less restrictive, you can go as far as using their source code to make closed software.