Generally, for passenger tires most TPMS systems by auto manufactures will illuminate when they are ~5 PSI below the recommended tire pressure. I run my OEM tires at 35psi all year around.
For the tire wear you are describing the previous owner ran the tire pressure FAR higher than 37psi. Running your tires at 26psi can be very dangerous - the low pressure can cause far too much flexing/deformity in the sidewall which can cause it to explode especially if the vehicle is heavily loaded. That is the reason Firestone tires were exploding on Ford Explorers - Ford had the psi set at 28psi to improve the NHTSA rollover rating instead of improving the vehicle itself.
For the tire wear you are describing the previous owner ran the tire pressure FAR higher than 37psi. Running your tires at 26psi can be very dangerous - the low pressure can cause far too much flexing/deformity in the sidewall which can cause it to explode especially if the vehicle is heavily loaded. That is the reason Firestone tires were exploding on Ford Explorers - Ford had the psi set at 28psi to improve the NHTSA rollover rating instead of improving the vehicle itself.