Thank you for the question.  It sounds like you are doing quite a bit of work to help your parents in order to keep them in their home and enjoying their neat yard. That is a big job.  Unfortunately, weed removal and control is always difficult and they will grow back eventually.  Salt isn't a good choice for weed control. It destroys the soil structure, changes the pH, and makes clay particles more compact, or crust-like and reduces rain/snowmelt infiltration.  You want good soil structure for water to enter and replenish the water table for favorable plants and the rest of our ecosystem. Salt contaminated soils can be reclaimed by leaching water through them but clay soils may not be reclaimable because the clay prevents acceptable leaching. You might be thinking that this is the type of long term solution desired but you will have to consider the effects of so much salt in your parent's landscape.  If the fence ever comes down, you might wish something would grow there.  With enough use, salt ruins the soil for everything else.  Also, if the soil is more permeable than you think it is, the salt could wash down into underground water supplies or wash into creeks or rivers where it would be very toxic to wildlife.  It could also spread to grass or other beneficial plants your parents would like to preserve.  

Unlike regulated herbicides that tell you exactly how much to apply, when to do it and so forth, salt doesn't come with this information because it's not regulated as such.  If you apply some amount, you would effect the aboveground portion of the weeds but not the roots.  More would need to be applied to kill the roots, but exactly how much?  An herbicide like Roundup would be effective and probably no more expensive than salt but you would have to periodically apply. It has the added benefit by being inactivated by soil.  Both salt and conventional herbicide will leave you with brown, burnt looking foliage which isn't very pleasing to the eye.  

There isn't a permanent, safe, low effort herbicide but perhaps some other options could be considered.  Maybe your parents would enjoy looking at perennial plantings at the base of the fence.  Some of the native grasses are beautiful and are very low maintenance other than weed whacking them down in the spring. Once established, they are very drought tolerant and provide food for birds and pollinators.  Of course, you would have the initial startup effort of preparing the soil, buying and planting the chosen option, watering, and weeding until established.  As the plants mature, they will crowd weeds out and you could mow right up to them, eliminating trimming.  If they don't like grasses, there are many other options.  Here is a power point from Mary Meyer at the University of Minnesota on ornamental grasses for Minnesota.  It has some great photos http://www.extension.umn.edu/garden/yard-garden/landscaping/ornamental-grasses-for-minnesota/index.html

There is another product called corn gluten meal that acts, over time, as a pre emergent herbicide.  It can be expensive and would need to reapplied yearly. The pre emergent effects are best seen over several years.  It has the added benefit of providing a small amount of nitrogen to the soil as it slowly breaks down.  You would still have to weed but hopefully it would be less over time.  

Read this publication from North Dakota State Extension comparing a vinegar, salt, dish soap solution to glyphosate (Roundup) http://www.ag.ndsu.edu/cpr/weeds/homemade-herbicide-08-28-14  

Here is another publication from Colorado State Extension discussing salt in soils http://www.ext.colostate.edu/mg/gardennotes/224.html 

There are just no quick, easy, cheap, permanent ways to control weeds.  I hope the information here gives you some ideas.  Good luck.

Thank you for contacting Extension.