Bitcoin is independent in value. It can be in the form of other currencies or medium. So if USD falls, people will tend to convert bitcoin in some other currency other than USD. Bitcoin holders who are residing in the US and/or using bitcoin in transactions in the US will be affected. They will get less than what they are supposed to get before USD falls and/or will suffer from loss in transactions and exchange.
Fall in American dollar generally bring increase in the market value of Bitcoin. After the fall of US dollar one can not easily achieve and afford Bitcoins as its price will have increased after the fall of American dollar. One can afford Bitcoin easily if the American dollar goes high so that price of Bitcoin will decrease and will be affordable easily by a common person. Fluctuations happen in the market and you should keep updating with the market.