When the SHTF, unfortunately your vehicle may do the same, leaving you with a primary mode of transportation that consists of walking followed by more walking. The more you walk or hike, the more stress you will be putting on your feet, which can rise exponentially if you are not acclimated to such activity. This can result in foot pain and other issues that will need to be addressed in order to enable your feet to hold up to the new tasks set out before you.
Since having healthy feet equates to being mobile, foot care is of the utmost importance and should not be put off. There are simple steps you can take to get your feet into tip-top shape, the first of which is buying well-fitting shoes and breaking them in properly. New shoes can be snug in places and may rub and cause blisters. This needs to be overcome in order to not only toughen your feet up but also make those shoes wearable for lengthy periods of time. Break in new shoes by wearing them around the house for a little while at a time until you've built up an ability to tolerate them without pain, rubbing, or blisters. If you begin to get blisters during the breaking in period, use band-aids, moleskin, or even duct tape if you must to protect your feet but be sure to keep your efforts up until your shoes fit well and feel comfortable.
Something else that can make shoes uncomfortable and affect fit is your toenails. If allowed to grow too long, toenails can make wearing certain shoes uncomfortable. Toenails may also become ingrown which can result in a painful infection that could need routine care at a minimum and might escalate to needing medical care. Having a toenail rub on the inside of your shoe overtime can cause the toenail itself to dislodge from your foot, which will expose raw skin and create a painful situation that could easily become infected. To avoid these issues, keep toenails trimmed at a reasonable length and file down jagged edges as needed.
Your feet will also need to be kept dry. Not only will wet skin rupture and blister more easily, it can also become infected and plagued by Athlete's Foot or necrosis (Trench foot is a good example of this). To prevent this, change socks frequently, as in every few hours. Socks that wick water away from your feet may be a useful addition. Feet can be kept dry through the use of powder as well but be sure to sprinkle it directly onto feet for better coverage and thus better results.
The bottom line is that you are going to need your feet, so you best take care of them now in order for them to take care of you later. The more work your feet are used to doing, the easier they will handle continued work in a survival situation, so get out there and keep moving, even when the couch calls your name. Keep your feet as comfortable and dry as possible in shoes that are broken in and fit to your feet and you will have far fewer issues down the road that could stop you in your tracks.