On Southwest, if the fare lowers after you purchase, you may request a credit for the difference. That credit is re-useable only within 365 days from when you originally purchased your tickets, not from the date the fare lowered. In other words, all travel using the original funds must be completed within 365 days of the original date of purchase. The lower fare must be available on your exact flights on your exact travel days. If the fare is lower on other flights on your travel days, that doesn't count.
Southwest's credits are fully transferable, so if you do not have another trip before the expiration of the credit, anyone else can use the value of that credit toward their ticket and pay you the value of the credit. Southwest credits are not redeemable on their website, so you can't use them for an Internet-only fare. However, if the lower price you found for your original ticket is an Internet-only fare, Southwest will issue the credit.