If jobs were interrupted due to insufficient disk space, they most likely exited completely. This depends on the way they were programmed, but I can't imagine any process waiting for user input before exiting due to failed write operations or other symptoms of a full disk.
There's no way to "resume" other than starting the processes again.
The only possibility you have is when the process (whatever it is) is aware of what output it has already produced and where it needs to start again. For example, the process could scan its output for already existing items and then continue where it left off. But no process does this by default, you need to explicitly program it this way.
It all depends on what exactly this process is, what it takes as input, and what output it produces (so, if we knew that, we could probably help you better).