[V8] Breather hose?

[Kevin Wahaus]

I noticed today a rubber hose on the top front of the engine that looked very oily/greasy. When I went to wipe it off, it pretty much disintegrated in my hand. I replace two rubber hoses last year when I replaced the valve cover gaskets, one in each valve cover. This one is in the front. Have no idea, but I’m thinking it’s part of the breather system and likely failed to an oil leak somewhere else that has it continually dosed in oil.

Any help? Is it ok to run the car or should I park it until I can find a replacement?

Kevin