Drainage and landscaping?

[cbishop]

I am in the process of landscaping my back yard.

We have fencing on the East and 1/3 of the way on the South (both are neighbors fences).

I would like to landscape all the way to our property lines so I can avoid trying to mow against the fence.

BUT...my spouse wants to leave some grass next to the fence to help with drainage. He's worried that if we have just plants and mulch that when we have a heavy rain that the mulch will get carried away.

Does anyone have a suggestion as an edging for the backside of a bed to keep everything in?

Thanks