Labour’s annual conference has voted to make it easier for local party members to deselect sitting MPs.
Until now, Labour MPs only faced a reselection contest if 50% of a constituency’s local branches and affiliated unions voted for it in a so-called “trigger ballot”.
Delegates in Liverpool voted for that threshold to be reduced to 33%.
The deselection campaign is seen by some Labour MPs as an attempt to “purge” critics of Jeremy Corbyn.
Those on the left of the party say they are out of step with the direction of Labour and point to the fact Mr Field lost a vote of confidence among members of his local constituency party in Birkenhead in July.
Other MPs including Kate Hoey and Gavin Shuker have recently lost no confidence votes, although these have no official force in the party and are not the same as “trigger ballots”.
Supporters of the new rules voted through on Sunday say they will end the “job for life” culture, while others said they do not go far enough.
But calls during the debate for compulsory open selection contests before every general election were not heeded.
Conference delegate Steve Arloff, from Bradford West Labour Party, said Labour MPs should not assume they have “some God-given right to be selected unopposed, expecting it to be a job for life”.
He went on: “Many sitting MPs who have lost the respect and confidence of local parties cling on to their positions in Parliament with scant regard for the people who work their socks off to put them there.
“Hundreds of thousands of us members demand that things are done differently.”
Unite general secretary Len McCluskey explained his union’s position by saying it wanted to offer 100% support to Mr Corbyn.
He said: “The proposition being put forward by our leader is something I am prepared to trust. There are certain MPs who are almost asking to be deselected.
“They really don’t want to be part of this exciting transformation that is taking place.”
Earlier, deputy leader Tom Watson told Sky News’s Ridge On Sunday that mandatory reselection would be “very destabilising for the party”.
“We are potentially close to a general election, maybe any day,” said Mr Watson.
“What we don’t want is MPs having to defend their positions in their local areas when they could be campaigning in Parliament for social policy that affects the many, not the few.”
By Iain Watson, BBC political correspondent
So what was Sunday’s row over MP deselections at the Labour Party conference really all about?
First, it speaks to the increasing tensions within the party’s left wing on how best to solidify the changes Jeremy Corbyn has introduced.
But what upset many left wing delegates was what they saw as an old fashioned stitch-up worthy of the Blair era.
They were given a straight choice between accepting or rejecting the NEC compromise – and no opportunity to vote for open selections.
Which brings us to the second point: the row tells us that there are now far more delegates on the left of the party than in previous years, even after Jeremy Corbyn became leader.