Consequences of having too low tyre pressure

There is flexibility in tire pressures. Try the lower pressure, keep an eye on how compressed your tire is. If it feels like bumps are hitting the rim increase the pressure. A quick ride around the block should tell you if the pressure you choose will work. If you bring a pump or other tire airing tool on your ride you can adjust on the road.

40 to 50 PSI on your new tire will probably be fine.

As tire pressure goes lower the chance of pinch flats goes up. At an the extreme end the tire will slip and spin the tube (for tubed tires) possibly cutting the valve stem.

I've run off road mountain bike tires with as little as 10 PSI with no ill effect (they were 2 inch tires - so further to go before pinching).

What are the consequences of going below the recommended lower limit (50)?

Pinch flats. If you ride hard over an obstacle, the low pressure inner tube will develop a pinch flat that causes a "snakebite" puncture on the inner tube.

If you ride tubeless instead, the tire will bottom out and has a risk of rim damage. (Every pinch flat on tube-type tires is also a risk for rim damage.)

I ride 100psi on 28mm tires (though I inflate so rarely that occasionally the pressure can go as low as 75psi due to natural air leakage). If I scale linearly inveresely to 37mm, I get 75psi as a good pressure to use in initial inflation (and reinflation is required at 55psi).

If you inflate below 50psi, you are already below the recommended limit for reinflation (55psi).

I'm a rather heavyweight rider who has a tendency to ride fast across every obstacle, not wanting to lose speed. If you don't ride as hard and your weight is average or lower than average, then I could understand less than 50psi. Otherwise I can't understand such low pressures. Besides, the lower the initial pressure, the lower the pressure will be when you reinflate (and if you reinflate every 2 weeks, the pressure will be very low then.)

The biggest risk of underflation is pinch flats. Pinch flats occur when the tube gets pinched between two layers of the tire. The design of the tire influences the minimum and maximum pressure. Size, material and intended use come into play along with the average rider weight the engineers used in their calculations. If the rider is well below what would be deemed average then you can reduce the pressure to an extent. I would start at the minimum recommended pressure and if need be drop it a couple of pounds per ride. You want to avoid being so low that pinch flats are an issue or you start riding on the sidewalls.

As others have answered already, the most common problem with low pressure is pinch flats

I think with thick and inflexible sidewalls it can also damage the sidewalls of a tire over time. However if you have flexible, lightweight tires (e.g. cyclocross/gravel or performance oriented MTB tires) this shouldn’t be a problem.

At very low pressures the tire can “roll off” the rim in tight turns.

I think I’ve written this on StackExchange several times, but my favorite method for gauging minimal tire pressure is to put the front wheel on a sharp corner (e.g. edge of a curb or stair) and push down on the handlebars with your whole body weight. If you can press it down all the way to the rim the pressure is probably too low, unless you ride very carefully.

Of course low pressure increases rolling resistance, but with good, performance oriented tires the increase is surprisingly low.

The Schwalbe Smart Sam is a pretty good and supple tire. 40 psi (2.8bar) is low for a 37mm tire but can still be fine with a lightweight rider (how light are we talking here? 50kg? 60kg?) and bike. But you should be careful when riding over potholes, roots, tram tracks etc.

As a 65kg person I went as low as 2bar on 33mm tires in cyclocross.

The tyre itself can be damaged when run for a too low pressure. That will be highly dependent on the tyre construction.

With tubeless tyres you can see the consequences when the sealant starts to penetrate the sidewall: White foam around tubeless tires

One problem is rim roll-off, which can also be described as squirm.

This is probably not going to happen at 50 PSI, but if your tyre is very low on air, going around a corner can feel awful. The tyre tries to follow its original track while the rim is forcing it to turn, so a low-pressure tyre can be "wrung" between the two.

It's an unpleasant feeling and you have to stop immediately to add air.

Apart from the key points users have mentioned above, too low of a PSI will also cause excessive heat on the sidewall due to increased friction as the tyre contracts and expands under load. This will lead to severe damage (namely, sidewall damage which begins first on the inside of the tyre as you'll see chunks of melted and broken off pieces of rubber).

Efficiency is reduced a lot.

Turning can become less controlled at high speed, as the tyre deforms sideways against the road from being too soft: if you turn the front of the bike, the back will try to keep going forwards, reducing your turning radius at speed.

Low pressure will cause the rim to hit stones and corners, causing a pinch flat.

If you have a super durable and light tyre, the rubber bending in the middle will fatigue the side wall material a bit faster, although it won't pop unless the rubber it's old and fragmenting.

Whatever is safe against pinch flats should be Okay, a bit less than MFR specs is fine, but much below that, it will pinch on a stone in the gravel. The front can be flatter than the back to be he same shape while riding, because the back carries more wieght.