If you were asking if you should buy silver for an emergency fund, I'd say no. But, you already have it...
Note: I wrote most of the below under the assumption that this is silver bullion coins/bars; it didn't occur to me till the end that it could be jewelry.
Both of you have good arguments for your points of view. Breaking it down:
1. A very good point. And while she may not be irresponsible, maybe the invisibility of it is good for her psychology? It's her's, so her comfort is important here.
2. Good. Make sure it's explicitly listed on the policy.
3. Bad. I think it will as well, at least the long run. But, this is not a good reason for an emergency fund -- the whole point of which is to be stable in case of emergencies.
4. Good. Identity theft is a concern, though unless her info is already "out there", it's insufficient for the emergency fund. And besides, she could keep cash.
1. Iffy. On the one hand, you're right. On the other hand, Cyprus. It is good to remember that money in accounts is in someone else's control, not yours, as the Cypriots found out to their chagrin. And of course, it can't happen here, but that's what they thought too. There is value in having some hard assets physically in your control. Think of it as an EMERGENCY emergency fund. Cash works too, but precious metals are better for these mega-upheaval scenarios. Again, find out how having such an EMERGENCY fund would make her feel. Does having that give her some comfort? A gift from a family member of this much silver leads me to assume that her family might have a little bit of a prepper culture. If so, then even if she is not a prepper herself, she may derive some comfort from having it, just in case -- it'll be baked into her background. Definitely a topic to discuss with her.
2. Excellent point. This is precisely why you want your emergency fund in some form of cash.
3. Bad. You can walk into any pawn shop and sell it in a heartbeat. Or you can send it in to a company and have cash in days.
4. Bad. If you know a savings account that pays 3%-4%, please, please, please tell me where it is so I can get one. Fact is, all cash instruments pay negligible interest now, and all such savings are being eroded by inflation.
5. Maybe. There is value to looking at your net worth this way, but my experience has been that those that do take it way too far. I think there's more value at looking at allocation within a few broad "buckets" -- emergency fund, savings (car, house, college, etc), and retirement fund. If this is to be an EMERGENCY fund, as per point #1, then you should look at it as its own bucket (and maybe add a little cash too).
Another thought to add:
This is a gift from a family member -- they gave her a lot of silver. Of course it's your SO's now, and she can do whatever she wants with it, but how would the family member react if she did liquidate it? If that family member is a prepper, and gave her this with the emotional desire to see her prepped, they may be upset if she sold it. It just occurred to me this may be jewelry. Your SO may not have sentimental attachment to it, but what about the family member's sentiments? They may not like to see family silver they loving maintained and passed on casually discarded for mere cash by your SO. Another thing to discuss with her.
Generally, you are right about not keeping a 6 month emergency fund in silver. But there are other factors to consider here. There's also the fact that it's already bought -- the cost of buying (paying over market) has already been taken.
Edit -- so it's silverware
Ah, so it's silverware. Well, scratch everything, except how the family member feels about, which now looms large.
This doesn't have much value as an emergency fund. Nor really as an investment. If you did keep it as an investment, think of it as an investment in collectibles/art, less so in precious metals.
If no one will get upset, I'd say pick out the nicest set to keep for special occasions, and sell the rest. Find out first if it has collectible or historical value. It may be worth far more than the pure weight in silver. Ebay might be the way to go to sell it.