I always found pennies all over my house and all the time, and I always assume we (my husband, I, the kids) drop it. Every place I ever lived, btw.
My youngest has fun filling his piggy bank with them every time I get ready to vacuum. He is the penny picker upper.
Now... if I ever found an engagement ring, or any kind of female ring, around my bed, any side, that went unclaimed by everyone I know and everyone who's ever been in the house, I'd be very suspicious because:
A- Either the person who dropped it didn't realize or miss it yet.
B- Or that person did realize but cannot claim it because he/she was not suppose to have the ring, or was not supposed to BE at your house and much less around your bed when he/she lost the ring.
C- Someone is pulling quite a prank on you guys. Is the ring an expensive one or just some cheap jewelry?
Chances are, someone you know, knows exactly where that ring came from and is just not telling you.