The answer to this question is quite surprising: use an ice axe. The self arrest works nearly just like in a icy situation.
I taught myself this technique, behind Bill's Barn under Tryfan in
early 1963, with a gang of mates, all of us having recently acquired
ice axes, by repeatedly throwing ourselves down a slope of pure water
ice. By the end of the afternoon we could break ourselves within a few
feet of crashing into the dry stone wall at the back of the farm from
a totally uncontrolled free fall.
A fall on frozen earth with stones embedded would be uncomfortable but
I believe that an ice axe arrest would work in non snow and ice
conditions, my axe was longer than the current axes, but not as long
as those of a generation before (...)
From Walking forum
When traveling through steep terrain, soldiers should be trained in
the use of the ice axe for self-arrest. The axe can be used to arrest a
fall on solid ground, grass and scree as well as snow. It may also be
used as a third point of contact on difficult terrain. If not in use
the ice axe is carried in or on the rucksack with its head down and
From Wilderness Survival
So, why the heck would you carry an ice axe while walking besides a grass slope? An ice axe could be used as a walking stick.
In its simplest role, the ice axe is used like a walking stick in the
uphill hand, the mountaineer holding the head in the center, with the
pick pointing to the rear.
From Wikipedia - Ice axe
No tools attached
If you don't have any tools, you should use this technique:
If (one) slips or stumbles on sloping terrain (hard ground, grass,
snow, or scree) he must immediately self-arrest, digging into the
slope with hands, elbows, knees and toes. If he falls backwards and
rolls over he must immediately try to turn over onto his stomach with
his legs downhill and self-arrest with hands and toes.
From Wilderness Survival
The hop-skip step
or how to descending grassy slopes to avoid falling in the first place:
(2) When descending a grassy slope, the traverse technique should be
used because of the uneven nature of the ground. A climber can easily
build up too much speed and fall if a direct descent is tried. The
hop-skip step can be useful on this type of slope. In this technique,
the lower leg takes all of the weight, and the upper leg is used only
for balance. When traversing, the climber’s uphill foot points in the
direction of travel. The downhill foot points about 45 degrees off the
direction of travel (downhill). This maintains maximum sole contact
and prevents possible downhill ankle roll-out.
P. 57 Wilderness Camping & Hiking - Paul Tawrell