If you can find a sewing needle, you can very, very carefully try to drag it out up against the nail above. I had to this exact thing once. Do not accidentally cut or stab yourself. Although the chances are low that it'd become infected, it's still an item with potential to harm.

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Even as such, I suggest washing it after.

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If it's close enough that you can use duct tape... Well. Try getting it stuck to that and pull.

This was my toe, most recently, but have had splinters everywhere lol. I soak in as hot of salt water as you can stand for 10 mins or so. Then use a sewing needle or cut back the nail with clippers if you can. My toe had dirt underneath the nail nearly to where it begins to grow, I fell down a creek hill. My sister laughed 5 minutes before she helped me up 😂 I repeated salt soaks and clipping, digging with tweezers and a needle until it was out. Yes it did bleed, no I was not going to the doctor for it. Peroxide and alcohol kill skin, advise against those if possible. Betadine is OK, but rinse off after or causes irritation. I used a bit of natural neosporin and a bandaid on mine. I have a high pain tolerance and determination