Well, I've heard sound would faint in bowed strings instruments if note played is too long, and player runs out of bow. Is this true? and at which tempo would this occur?
It depends on the dynamic you are playing in, but you can maintain a good tone at a slow pace with practice. Louder volumes require more bow and limits the duration you can hold one bow stroke.
Practicing playing from frog to tip while keeping a steady count teaches your arm how fast it needs to go to maintain the bow for the duration required.
As commented by Todd, if you end up with a duration too long for you, changing the bow discretely on a beat is an acceptable technique.
I'm sure there are players that can hold a whole note at Grave without loss of tone.