It's happened to me before on my old LG G2 on Verizon network. I had to take it into the shop and they were able to recover my contacts. But since then, I only use my google contact list. Never have to worry about losing contacts unless I lost my gmail. :P
Yes you have to go into settings. Shows everything including contacts not sure about backups I believe so. Click on account right corner where gmail name is.
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Everyone got a plan until they get punched in the face.