Throughout the years Arsenal have lost many players who went to the USA to study and play, starting with the one and only Kelly Smith who went to Seton Hall.
The current generation have been doing great and are playing in the NCAA tournament right now.
Anna Patten

A right-back or centre-back, who was a key player in the Spring Series 2017. She scored the winning goal for FSU in the first round and could be a title contender as her university has a strong squad.
She is also a u-20 bronze medal winner.
Lotte Wubben-Moy

Another defender who can also play in midfield who was key for the team in the 2017 Spring Series. She is currently playing for another title contender, UNC.
Lucy Parker
Another defender who plays for LSU, she scored the game-winning penalty against Boston University to send her team through to the second round.
https://twitter.com/LSUSoccer/status/1061735847664500737
Shannon Cooke

Also a defender, Shannon plays for LSU and recently scored a rocket from 40 yards:
https://twitter.com/LSUSoccer/status/1059187621627420672
Chiara Ritchie-Williams

Another LSU defender, she can play at right-back or centre and is also a key player for the Tigers.
Tinaya Alexander

A winger for LSU, one of the four ex-Arsenal players at that university.
Laura Hooper

An attacking midfielder who plays for Seattle University, her team got knocked out in the first round by one of the favourites.
Jordan Littleboy

A central midfielder who plays for Hofstra and helped her team upset Boston College 4-1 away.
Miri Taylor
Another central midfielder playing for Hofstra who has scored important goals this season.
https://twitter.com/HofstraWSOC/status/1049011248606531584
Georgia Allen

Also in the USA and playing for Syracuse. I interviewed her during the u-20 world cup. I also spoke to Anna Patten during the World Cup about her time at FSU.
All the women have chosen to play and get a degree in the USA. They might come back to England after their senior year as the NWSL does not offer many options with the number of foreigners is limited for all the teams.