Faring and fearing are easily confused words.
The spell-check application of most word processing software programs would not catch a slip-up of these two words. Spell-check is looking for words that aren’t in its dictionary, and words that resemble words in its dictionary but are possibly spelled wrong. Spell-check isn’t perfect. It doesn’t know and can’t guess what word you wanted or what word you meant, it can only judge the words on the page. If you used words that are all spelled correctly, it gives you a pass anyway.
Autocorrect suggests words that start with the same letters. It’s suggesting what word you may want to save time, but quite often, its suggestions are pretty off base. They don’t help you out, but they do make you laugh.
Faring is a gerund form of the verb fare. To fare means to experience negative or positive outcomes.
Fearing is a gerund form of the verb fear. To fear is to be afraid or scared of something or someone, or to experience anxiety about bad outcomes that could happen.
The following story uses both words correctly:
Ferris is fearing that his family’s farm isn’t faring well in this heavy flooding.