In general, if a work authorization card is lost, stolen or destroyed, it should be replaced. There may be certain practical exceptions to this rule. For example, a DACA recipient who has to renew annually, and who is close to time to file for the renewal, may decide just to wait a little bit and file for the renewal (not a replacement). The filing fee is the same for both a replacement and a renewal.
Having an actual employment authorization document (card) is valuable as new employers are supposed to request it for employment eligibility. In Florida it's helpful for obtaining a driver's license.
While it is advisable to actually always possess a work card, the need/time to request a renewal will depend on a person's specific immigration case. Work eligibility is not revoked just because a card is lost. The card is just tangible proof of eligibility.
Cards, indeed, all of an individual's immigration records, should be copied and safely stored. Backing up to the clouds can later save people money and time.