Here’s my explanation, if I understand what you’re asking correctly.
Christ, of course, is the ultimate exemplar for someone who offers up suffering for the benefit for others.
He did that, as he did everything else while on Earth, for us. His mission was to teach us how we can attain salvation, by following Him and adhering to the many lessons He taught, through His actions and His Words.
As a cradle Catholic, I was brought up by very good parents who knew their share of suffering. My mother, in particular, lost a brother and a daughter in the span of a year. She grew up in the depth of the Depression, and when her father died in the 1940s, in the midst of her college education, she had to immediately drop out in order to support her family.
She also had to deal with raising a houseful of intelligent, willful kids and went to work as a teacher midway through so that my parents could send them all to college. She also lived long enough to see another one of her children die. She had a number of near-misses on other occasions, all involving lengthy hospital stays.
She always stressed the importance of offering up her suffering for the souls in purgatory, just as we look to the saints and our Blessed Mother for intercession.
I’ve always tried to cling to that ideal, knowing that, no matter how much I suffer, I can always volunteer to take the place of another. I’m afraid it isn’t an easy thing to do; often, I get too wrapped up in my own problems to think of anyone else, which is shameful. But the ideal is still there.
I, for one, am terrified of flying. Unfortunately, my job takes me to assignments in distant cities that require air travel. I try to offer up any anxieties to Our Lord for those who can’t help themselves – i.e., those whose sins are being purged before their entrance into Heaven is granted.
It helps.
I don’t know if any of this is analogous to the situation you described, but I hope it helps.
God bless.