Frangible ammo was initially designed (for the mass marketing,) to allow indoor ranges, an option against lead dust in the air. It has evolved a bit into ammo for shooting steel at closer distances as well as other purposes. Such as the stuff blume mentions. A type that allows live fire upon each other for training.
There are different types of frangible available now.
I didn't watch the video above,, but I have studied some of that stuff,, to see if I had any need for it.
Now,, shooting steel,, like what blume mentions at my range.
We shoot USPSA here,, and steel is an allowed target. However, there are rules, specifically shown in the rule book on distances a steel target must be from a shooter. A minimum of 27 ft is required,, and most USPSA match directors prefer at least 3 ft more,, as a "fudge factor." (Example; A hard charging shooter runs to a fault line where steel must be engaged from. As he's shooting, he also is moving so hard & fast that he passes the "fault line" and goes forward, by a step. If the steel was engaged & a fragment were to come back,, the 27 ft rule should help a bit.)
We shoot a lot of steel here.
As such, blume is right,, you will see discs of lead splatter that impacted a steel target, from about a dime to a bit larger than a nickle on the ground all around where steel is shot. When a softer lead bullet strikes steel directly, it does fragment, and as the energy is expended, what doesn't fragment, ends up being that disc. Both powder coated & normal lubed lead bullets do this easily. Jacketed bullets will also fragment,, but not in the same manner. HP's fragment a bit more than a solid nosed bullet. But we also find flattened jacketed pieces as well as all sorts of pieces.
The distance thing allows for energy to be absorbed,, and if any pieces do bounce back towards the shooter, (or others,) it is normally reduced enough to where any potential injuries are minor.
But often,, people do get a fragment that bounces back to a shooter, a RO, or even others standing behind a shooter watching. I was at a SASS match long ago, where they had a LARGE steel "dump target" that was being shot at,, and I was over 100 ft away & got a fragment to hit me. It's why we also require eye protection.
All ammo can & will fragment depending upon the type of target it hits. Some will just do it quicker, or disintegrate into a dust,, if it hits a hard steel target vs., say sheet rock, or plywood, or whatever.
So, as to the OP & about use of frangible ammo for SD inside a home.
There are a LOT of factors & variables you have to understand about such potential uses. Houses are built where the exterior has brick, masonry, rock, Smart Siding, Hardiplank, aluminum, or vinyl in general. Inside that, us normally the exterior sheathing, insulation, then 2x4 studs, with whatever interior wall material chosen. Interior walls can have thin paneling, sheet rock, wood, or other materials.
BUT,, totally interior walls are not built the same as exterior walls. Quite often, they are mostly 2x4 studs, without insulation, and whatever interior wall material is chosen. In todays world, the most common interior wall material is sheet rock. And even that is in different thicknesses. An exception is commercial buildings,, (motels, apartment complexes, etc.) where aluminum studs are used in place of wood studs.
Next,,, consider angles of the bullet paths. Direct or at an angle. How many layers of whatever materials are use and at what angles? A direct hit on an interior wall, will most often only hit 2 layers of sheet rock, if hit between the studs. Very little to stop a bullet. Add in the stud. If hit "centered,," you have an additional 3.5" of wood to allow a bullet to expend energy. But a partial hit has less mass to penetrate. Add in an angle,, and you may actually get to hit 2 studs,, but if so, it'll be still less than a direct hit on a stud. (Think aiming along a wall, and firing to where the bullet goes through the wall and into the next room.)
Frangible ammo has it's place,, but to think it's a end all, be all SD answer,, is not thinking of all the potential issues.
About 40 yrs ago,, I did my own testing of SD ammo that I had loaded. I had read about using .38 spl. soft lead HB wadcutters, inverted, over a mild to moderate charge of powder. I shot wet telephone books, plywood, water jugs, and sheet rock. I also tested another SD ammo idea,, by loading 3 pieces of #1 buckshot in a Speer shot capsule, over a mild to medium charge of powder.
Both loads allowed me the potential of stopping an attacker at close range if I hit the attacker. Wet phone books, and water jugs showed that potential.
Other materials showed me that all can & would likely penetrate the wall materials. But the energy would be reduced somewhat,, thereby reducing the possible injuries on the other side of a wall.
But the biggest thing I learned,, was to "NOT miss my target!" That way, I would reduce the potential injury to an innocent person, (my family) greatly!
Too many variables to where there is no one answer to such a complicated question.