Can 2 different OOV words get the same vector in FastText?
TL;DR
Theoretically it is possible, but it is unlikely.
1) Uncommon subwords
word1 = 'iiii'
word2 = 'jjjj'

word1_subwords = ['&lt;ii', 'iii', 'iii', 'ii&gt;']
word2_subwords = ['&lt;jj', 'jjj', 'jjj', 'jj&gt;']

In this example, there are basically 6 subwords: ['&lt;ii', '&lt;jj', 'iii', 'jjj', 'ii&gt;', 'jj&gt;'], but these are not common subwords in general. So, there is a possibility that the embedding for all the subwords is the same (e.g. [0,0,...,0,0]), making their sum all the same.
2) Homographs
word1 = 'lie' # meaning: tell something untruthful
word2 = 'lie' # meaning: to rest on a horizontal position

In this example, there are two homograph words. These are different words but they have the same spelling. Since FastText only take syntax into account, they will have the same subword embedding sum.