Reading & Writing to the same file from terminal

Question

Given a file foo

1
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5

Can someone help me understand why the following results in an empty file?

cat foo | grep 1 > foo
wc foo
0       0       0 foo

whereas the following appends fine

cat foo | grep 1 >> foo
cat foo
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1

I'm not surprised with the functioning of >>, but with > my expectation was that the file will contain just the output of cat foo | grep 1. What's the underlying implementation detail that results in this behaviour?

cat foo | tee foo

on the other hand does not empty the file.