On the back of the clasp, I see the typical "M in the shell" mark of Mikimoto pearls. Given that this is a strand you know belonged to your MIL for many years, I think we can assume it's Mikimoto, even without the documentation or the box.
(If this were a strand you bought on eBay, you'd have to consider that a) there are fake Miki clasps out there, and that b. ) real Miki clasps can be strung onto non-Miki pearls, so the lack of documentation would be more concerning.)
They look nice enough...but given that it's a sterling/ pearl clasp (as opposed to a gold clasp /diamond clasp), these are not Miki's highest grade. They are still very nice.
They really need to be restrung. Silk gets old and grimy and then it's weakened and can break, and the necklace be lost. The necklace seems to be knotted only at the end few pearls, not unusual for this sort of graduated strand, so it's not hard to restring them-- only a few knots to do! You can easily do it yourself at low cost (see tutorials on the Lowly Beaders Club forum.)
Whether you do it yourself or take them to a jeweler to restring, I'd factor the cost of restringing into the value of the pearls, as they are not safe to wear until they are restrung. You can call a local jeweler to ask what they would charge for restringing; $3/inch is not unusual.
As to value, IMO all the jewelry should probably be valued at resale value -- based on actual sales prices achieved. Check out eBay and other venues (Ruby Lane, Etsy, etc.) for what similar items sold for.
For example, here are the current eBay search results for
sold Mikimoto graduated pearls that are not double strand and don't have gold or diamond clasps; I notice items with original box and documentation, and sets that include earrings, seem to sell at a higher price:
https://www.ebay.com/sch/i.html?_fr...nd+-double+-gold+-18K&LH_Complete=1&LH_Sold=1