Disclaimer: This content is the result of my having survived several emergencies of varying effect sizes. Most of these ideas are rules of thumb, and not canned answers. As in any emergency your best outcome will be if you keep calm, consider many options, and flow from plan to backup plan as requried.
Physical security is important both for health and for cybersecurity. The security of medicines, food, and computers should be protected. Just as with cybersecurity, physical security exists on a continumm from more to less secure. It is quite typical for buildings to have keyed locks, deadbolts, and sometimes alarm systems. Additional physical security measures involve fences, cameras, security guards, and safes.
In many cases these physical security devices are arranged like layers on an onion. The most cursory measures are the outer-most while the most stringent measures are the inner-most and protect the fewest items.
It is a good rule-of-thumb to have similar security systems as your neighbors. If one has vastly less or vastly more security, one's home or building might become a special target.
As always, no physical security system is perfect, and the determined intruder may be able to find a way in. A good rule-of-thumb: if intrusions occur too frequently for comfort, then more security is called for.
Watchful and respectful neighbors are a strong deterent to crime. Consider forming a neighborhood crime watch. Community is especially critical in an on-going emergency.
Possible strategies include: knowing your local locksmith, leaving a key with a friend, obtaining rental or housing insurance for your valuables, storing the most critical papers in a firebox or in a safety deposit box at the bank. (Note that a bank has certain legal obligations in releasing the contents of a safety deposit box, so the contents may not be readily available.)
When using a key'ed storage solution, make sure you have extra copies of the keys to give to relatives and do not store the key right next to the storage solution. It is often sufficient to use big-data to hide the key, in-plain-sight, as it were, some place nearby but sufficiently far away from the storage unit to make accidental discovery improbable.
Be extremely careful not to hide the key from yourself! Locations are difficult to find or remember when a person is sleep deprived or anxious. Using memory crutches and routines can help solve this problem. Store like items together. To cement the location in your memory, revisit the location for several days in a row to remind your mind and body where the hiding place is. (A similar idea can be used for pin'ed storage solutions. Keep in mind that you may forget the pin, but do not stor the pin next to the card or device that it opens.)
Each of these strategies also introduce new vulnerabilities, so be sure to make multiple copies of critical paperwork and travel with it when necessary.
Also, remember to secure old documents to the best of your ability, i.e. old passports, ID cards, unused credit card applications. Some of these can be stored with your sensitive documents or shredded, as needed.