It is not clear that you would be required to train the person. It is possible the other person would train and you would be asked to help out by doing things the employer thought you were capable of.
As you described it, you walked off the job. So, you quit. Unless the interim duties were extremely different, dangerous, etc from what you had been doing - it was work you could do and it would have helped them.
It seems unusual to ask this of someone being let go and you may have felt it was too much of them to ask. Talking to them about just what was expected and for how long could have made a difference.
You will probably have to earn a specific amount before you qualify - something like 6x the weekly benefit rate you would have qualified for.