Do airlines have an obligation to transfer you if they book your connecting flights?

Hi,

If I have booked connecting flights through the same airline at the same terminal and with a considerable lay over time (>2hrs) and the first flight gets delayed reducing the transit time to under 1hr, will the airline hold the next flight till I am able to board it safely?

If not, do airlines refund the ticket for the second flight?

I wonder should airlines be allowed to book connecting flights below a stipulated time considering weather and other delays.