Britain's Prime Minister Theresa May arrives at Downing Street with her husband after Britain's election in London. If she is the leader of the largest party, there is a duty on her to seek to form government.
Mr Farron held on to his Westmorland & Lonsdale seat in Cumbria on a much-reduced majority, down from 8,949 in 2015 to just 777 now.
Some colleagues may be lining up to replace her, although a party source said the post was seen as too much of a poisoned chalice for the time being.
Party insiders are placing bets on how long May will last, less than a year after Britain's surprise referendum decision propelled her into Downing Street.
But elsewhere in the E.U.'s political establishment, there were questions over whether Britain, newly submerged in political uncertainty, could now even engage with the complex negotiations that lie ahead.
On Brexit, the DUP supports leaving the European Union but opposes a return to a "hard" border with Ireland - which could happen if May carries through her threat to walk away from the talks rather than accept a "bad deal".
Duncan Smith said the Conservatives would now concentrate on minority government negotiations.
"It will be hard to govern and it could mean another election later in the year", said Wyn Grant, professor of politics at the University of Warwick. "Remember, both parties are divided".
"The Conservatives have not yet broken the British system of democracy, but through their hubris and incompetence they have managed to make a mockery of it", it said in an editorial.
"May won't be able to make any compromises because she lacks a broad parliamentary majority", he said.
Scottish Conservative leader Ruth Davidson said she has received assurances from the Prime Minister over gay rights should the Tories do a deal with Democratic Unionist Party.
The lack of a decisive victory for the Conservatives also called into question how the United Kingdom will negotiate its exit from the European Union. This will allow us to come together as a country and channel our energies towards a successful Brexit deal that works for everyone in this country.
European Union negotiators will want to know who they're dealing with.
The Sunday Times reported that Chancellor Philip Hammond used a telephone call with Mrs May on Friday to tell her she should put jobs first in the Brexit negotiations - a coded attack on the immigration-focused strategy.
"How do you negotiate when you know that the position of the partner that you're negotiating with is extremely weak?" says Klaas of the London School of Economics.
In a humiliating night for the Prime Minister, Mrs May saw Tory ranks at Westminster reduced from 330 to 318 - with one constituency left to declare - while eight ministers were culled from the Government's front benches.
Before the election, May said on her official Twitter account that if she lost "just six seats" she would lose the election to Jeremy Corbyn.
"If, as the indications have shown and if this is correct, the Conservative Party has won the most seats and probably the most votes, then it will be incumbent on us to ensure that we have that period of stability and that is exactly what we will do".
The DUP is skeptical of Europe and is pro-Brexit.