Yes, this is a common colloquial usage, meaning that his friends were persistent in trying to help him keep from hurting himself. However, since it is colloquial language it's important to understand that it's not appropriate in formal contexts. You wouldn't use these terms when writing, unless you were writing casually to a friend who you know would understand them or writing to express dialog between two people speaking casually to each other colloquially.
A more standard or formal way of saying the same thing would be
After his suicide attempt his friends have worked tirelessly to make sure he doesn't try to hurt himself again.
After his suicide attempt his friends have been in constant contact with him to make sure he doesn't try to hurt himself again.