Say a random variable X is distributed as binomial(10, theta).
In the data, out of 10 trials, there are 0 successes (i.e. 10 failures).
How to calculate MLE for theta for such data?
How does MLE change when it is given that 0 < theta < 1 vs 0 <= theta <= 1?
The MLE for Bernoulli distribution is computed here.
In your case it leads to $\theta=0$. And MLE doesn’t change when you change from closed to open interval for $\theta$.