You are not restricted to just mulch. And I'm not sure what a mulch 'design' is. There are plenty of plants which would grow there if you made a deep flowerbed along the fence. If you give your location people can make suggestions.

Where do you live? There are plants that grow in the shade, but without knowing where you live, we cannot suggest anything. Please be pretty specific. We don't need your street but we do need the city, town, or community.

Sorry I’m new to this! We were thinking mulch because it is fairly easy to maintain. We just don’t know how to place it along the back fence.

I live in Canada - zone 3b. Thank you!!

Zone 3b spans quite a lot of Canada and quite a number of climatic classifications. What's your Province and closest city?

I'm Zone 7a, which ranges from my own almost-temperate-rainforest of Pennsylvania to semi-arid Texas and New Mexico. What I grow here--anything I want that doesn't mind wet feet except for a dry August--is very different from what I'd grow there--stuff that will tolerate low rainfall and low irrigation.

Mulch is not easy to maintain. I go through 30 bags a year on my tiny 1/8 acre lot. It’s backbreaking and takes weeks to get it all down. What about hostas? They do well in shade, are perennial so you (usually) only have to plant them once, and come in tons of varieties and sizes. And the more hostas you plant, the less mulch you need to cover. ☺️

Nearest city would be Calgary, AB. My backyard exposure is southeast, but unfortunately that area gets little to no sun due to the trees above. Grass is all dead unfortunately!

What design would everyone put at the back fence (whether mulch or plants)? Straight across? Curved?

I think curved is more interesting, but straight can be easier to mow, depending on your edging material.

It’s purely a style preference. Mine is curvy because I keep adding more plants and making the landscape beds bigger. Where ever grass wouldn’t grow, I’d add another hosta. 😳🤷🏼‍♀️

In most cases curved is better that straight lines. Shaggy bushes are better that formally trimmed plants, etc.

If you soil test, lime and fertilize as appropriate and plant shade grass you can have decent grass in the area also. If you plant hostas , ground cover and other plants that can be divided, over time you will have a source of new plants for free.

Though people do mulch only, it begins to be a PITA when it's discovered that it's not as pretty as plants and that the mulch must be replenished at least annually, at a cost and a bother. If you transition to plants, when their cover takes over there is not need for more mulch. There are plants that grow in the shade if you give them some help along the way.

Get free mulch from tree trimmers. you can cover it with better looking purchased mulch if you want it to look better.

From your picture, that looks like pretty open shade? Don’t give up and just do mulch. And please never do orangey mulch, only black/dark brown. We have a very shady back yard, with huge old Norway spruces and a Norway maple. We have euonymus alatus - winged euonymus or burning bush planted under the trees, along a weathered 6 ft. fence. They don’t get as bushy, and they really have only a hint of red in the fall, but they do okay in spite of getting no direct sun. They should be hardy where you are. Best bet for finding shrubs for this problem area is to take your photo to a local garden center and ask for suggestions. Here is a picture taken this morning - that’s about as much sun as our euonymus get! and a picture taken in June. Under-planted with aruncus/goats beard, hostas, and (yes, horror of horrors!) bishops weed. Before posts start coming in expressing outrage at planting invasive bishops weed, it’s been there for 15 years and while it has filled out, it has NOT been invasive AT ALL - too much shade and tree root competition, and it does help light up the shade.

There are lots of plants that would do well in your space. I've planted so many trees in my years (in North Dakota) that I've had to convert most of my flowerbeds from sun to shade plants.

Start researching, and start planting! You have an amazing blank slate - I hope you have fun developing a beautifully landscaped shade garden.