How To Make The "Almost Worst" Top Stair Stringer Connection Structurally Stronger
A common method for attaching the stringer to the floor joist is to toenail it or nail it at an angle on both sides of the stair stringer. Then goes on to give several suggestions for how to make this type of connection stronger.
One suggestion is to add a support board between the top stair stringer and the rim joist. Another suggestion is to use a hanger to connect the top stair stringer to the rim joist. Finally, suggests attaching a new piece of lumber to the top stair stringer.
Here are some bonus tips
Use treated lumber for any parts of the stairs that will be in contact with the ground.
Use full-length materials for the stair stringers.
Use hardware connectors to connect the stair stringers to the rim joist.
If you are worried about the wood splitting, you can pre-drill your holes or stagger your nailing.