UK Prime Minister Theresa May was clinging to power by her fingernails on Sunday after losing her parliamentary majority in last Thursday's election, as an agreement with the minority Democratic Unionist Party that would keep the Conservatives in power was still not finalized. May's co-chiefs of staff, Nick Timothy and Fiona Hill, handed in their resignations on Saturday following the disastrous election, called by May to strengthen her position ahead of talks to leave the European Union, but which in the end left her weakened.