What will it happen to infants who overstay in Thailand after entering the country with tourist visa? 

Nothing - Children under 16 (15 and younger) cannot be charged or penalized for overstay. 

 

However, being exempt from a fine / penalty does not mean they do not need a visa - thus, its still best to obtain the correct visa for them... either through their School or as a dependent etc.. unless you are just having a long holiday in which case, obtain a tourist visa. 

3 minutes ago, richard_smith237 said:

Nothing - Children under 16 (15 and younger) cannot be charged or penalized for overstay. 

It is under the age of 15 not 16.

Even though they can’t be fined they will have an overstay stamped in their passport, and it will be on their immigration record. It’s best to keep the child legal if you can.

On 5/24/2019 at 5:00 AM, elviajero said:

Even though they can’t be fined they will have an overstay stamped in their passport, and it will be on their immigration record. It’s best to keep the child legal if you can.

Not only that but some other countries (USA for example) will refuse you a visa if you have a overstay stamp in your passport from another country.