Here's a private key with 0.00001 BTC on it, no fee required to import it, but also not enough money to send it anywhere.
addr: 19bjqNiSWxMuCcbzcszS37BJfNMKLA7vh1
priv: L3Upbvtaij1xMmG2iXTokSgguAPy3c4fnR81xFcUKc2263hapovb
It seems to have been cleared out as soon as you posted it.

Be very careful in dealing things like this.
You do not need be careful because the person posting it needs to be trustworthy, you only need to be mindful not to accidentally reuse the address. After importing, Bitcoin Core will not give you this address when you use "request a payment", but you could do something silly like look through your list of past transactions and take the address from there when you ask someone to send you money. I never underestimate the ingeniousness of idiots.
Even for dust, someone will quickly snatch up and spend private keys I've posted before with a balance for fun. It's first-come, first-serve, since anybody can use the secret key to spend the money.