On this page of the Death Stranding guide, you'll find the answer to two pretty important questions - whether the multiplayer in Death Stranding is mandatory and whether you can continue to play offline (like in case of lack of connection to the Internet or to the game servers).
No, multiplayer in Death Stranding isn't needed in order to complete the game Moreover, Death Stranding does not require an internet connection to play the game (constant connection to game servers) You can start the game in an offline mode, or simply continue your campaign if the connection is lost.
Unfortunately, the offline mode means that some of the mechanics are unavailable. These can be found in the following section: How does multiplayer in Death Stranding looks like? in our guide - you won't see the movements of other players, be able to send and receive likes, use the equipment left by other players or exchange gifts with them. Having no access to these features won't disallow you to finish the game, but your progress in the campaign may suffer.
If you started an online game and lost your connection for some reason, you can try to log back to the game servers. Enter the pause menu, choose System and then press the Log In button. If the attempt is successful, you will get access to all multiplayer and social game mechanics. You will also be able to pick up left-over gifts (eg. likes awarded to you by other players).
It is worth noting that the loss of connection to the game server and switching to offline mode doesn't mean that you won't be able to access the objects of other players. The game will save other players' structures, signs, and vehicles - you can still interact with them. However, you won't see any new designs in your world. Once you manage to log back in, you can also receive various gifts, such as likes or materials from other players. "Rewards" of this type, fortunately, don't disappear.