With a 7/8 fractional rig the forestay load will be 1/8 down from the masthed and the aft stay fixing point.
At this distance from the top (and less) the mast is considered to be so stiff that the forward force induced by the head stay will be transfered to the back stay.

The same reasoning applies for a solent stay on a masthed rigged boat.

 

Rigs are all different, as are the masts they hold up. If you rig an inner forestay temporarily (for a storm sail, for example) on a masthead rig, the stresses involved may call for a backstay to counter the forward pull that might wrack the mast out of true. If the stick was stronger, maybe a backstay wouldn't be needed - but it would likely then be heavier, which might mean more rolling in rough weather - just when you'd want to be smoothing things down aboard by putting up a storm jib. A 7/8 rig might not require running backs for a variety of reasons. Maybe the mast extrusion is hefty enough, as just said, not to need them. Maybe there are jumper struts to stiffen the mast and spread the load at the top and thus make the permananent backstay sufficient. We have running backs that we consider using when the wind picks up over about 25, but we don't need them all the time because the section and jumpers keep the mast stiff enough in lighter winds. Everything's a matter of balance. We like the fractional rig because it provides a bit more sail shape control for the main, makes changing jibs easier because they're smaller, and enables us to reduce or increase sail quickly by reefing or unreefing the main without having to get out to the foredeck.

 

Many 7/8th rigs do use running backstays and/or checkstays. Jeff H can weigh in on the many advantages (from a sail trim/shape perspective) that a fractional rig offers - in fact do a search and you'll find many excellent articles on the topic already here. As Paul mentions, smaller more manageable headsails and spinnakers is another 'advantage'.

Whether or not a frac rig uses runners is really a combination: of the intended purpose of the boat (ie racing vs cruising), the flexibility and structural properties of the mast section used, the arrangement of the spreaders and shrouds (ie swept vs in-line) and the interest of the owner in pulling "extra strings".

Many of the current crop of production fracs use varying degrees of spreader sweep angles to aid in supporting the mast section and prebend - and provide some forestay tension without runners. Hunter is most extreme here, with severely swept spreaders and the B&R diamond stay pattern. Beneteau and others are using more moderate sweep angles.

A stiff enough, strong enough mast section will not need runners for structural integrity, but performance will benefit by using runners to tension the forestay. With a bendy top section above the hounds cranking on the backstay will induce mast bend without necessarily adding to forestay tension. Here is where runners serve a good purpose, directly applying forestay tension, and contributing to the precise shape of mast bend in combination with the backstay.

When cruising, however, runners need to be handled on each tack, and while gybing they can really be problematic if the end up getting snagged on the wrong side of the sail. Our boat, a 3/4 frac with a relatively robust section, is rigged for runners. We have chosen not to use them at the obvious cost of pointing ability, but the advantage of simplicity.

Production boats today are built to simplify sailing (eg.. roller mains - which don't really like mast bend much) and so most of their rigs are designed to function without runners... that doesn't mean they wouldn't benefit performance-wise from adding them.