A JSS of less than 50% is never (!) shown on any profile. Clients will not see your JSS when they look at your profile.
It is impossible for clients to NOT leave private feedback, they have to when they leave the public feedback.
You want to be very careful who you work with and stay away from the "bottom of the barrel" price segment (the nonsense of the "we pay you $ 3 for 300 words" variety) as such clients are almost invariably as mean with their feedback a they are with their money.
There are only 2 things that really hurt your JSS:
1.) Bad private feedback
and
2.) Contracts that never lead to any earnings (canceled contracts, fully refunded contracts, contracts that opened and stayed open for several months with nothing having (ever!!) been paid.
We've seen people recover from worse JSS scores. Because you had so few completed contracts, every single contract has a BIG impact. That means that just a handful of successfully completed contracts will have a huge impact. You do have to be super careful who you work with though.
Edited to add:
Whilst a low (below 50%) JSS does not show on a profile, it does show on search results.