Can I claim a loss on my 2018 tax return for Stock Appreciation Rights that expired in 2018?

[infandibulum]

Since "Rights" does not suggest that you actually own the stock, you probably had "options" to buy a stock. If that "option" expired in 2018, you no longer have a "Right" to buy it. Actually, I've never heard of "Appreciation Rights". There are only 'calls' and 'puts' derivatives. Your employer may have its own 'pet' name for employee stock options.
If it was a 'call' option, it may have had some value when it expired, but you'll have to check the account that it was held in to find out how much. A 'put' option would never have been considered an 'appreciation' option. And, I know of no employer who gives 'put' options to their employees.