Archaeological sites and ancient cities, now unpopulated, are usually established in SAF. If the site/city is under a modern city, it probably will not get an independent heading but will get headings such as "Rome (Italy) -- Antiquities" instead. If the site is needed as a heading, a subject proposal may be prepared. The Getty Thesaurus of Geographic Names is a good resource for these names.
Memo H 715 in the Subject Heading Manual from the Library of Congress deals with extinct cities. https://www.loc.gov/aba/publications/FreeSHM/H0715.pdf
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Available from ARLIS/NA:
Concordance of Ancient Site Names
(Topical Paper No. 2)
A compilation of more than 3,200 ancient site names linked together to show variant names for single sites. Included are variations in spelling, transliteration systems, historicity, and language. Originated as a pilot project of the ARLIS/NA Visual Resources Division Task Force on Authorities, formed in 1987. Edited by Eileen Fry and Maryly Snow. Available in both electronic and hard-copy formats. Electronic version available in Macintosh or DOS 3.5 in. formats for resident database or word-processing environment. (1995) 78 pages. Paper. $25.00. Diskettes $5.00 additional. ISBN 0-942740-13-0.
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Photo of Morgantina site on Sicily, looking toward Mount Etna, photo from March 2013. The heading "Morgantina (Extinct city)" is LCCN sh89002430 in LCSH.