Given some of the news that has come out since the election, I thought I would explain exactly what Clark is doing, how, and why.
There are 87 seats in the BC Legislature. The Liberals hold 43, the NDP hold 41, and the Greens hold 3. One of the MLAs will need to serve as speaker. You need 44 MLAs to have a majority.
The plan is this. Clark, as the incumbent premier, has the right to meet the house and test its confidence. All premiers do. Even if the NDP had won 60 seats, she still would have this right. It's simply custom that Premiers in Canada stand down when it becomes clear and obvious they will lose a confidence vote. The Liberals will put up a candidate for Speaker during this period. This means there will be 1 speaker, 42 Liberals, and 44 members of the Coalition (NDP-Green) that will vote on issues.
It is unclear if Clark will call a direct VONC (Vote of Non-Confidence) or will simply try to pass a throne speech, which itself, is automatically also a VONC. The result will, regardless, be the same. The VONC is expected to pass, 44-42, and Clark will be forced to resign as Premier.
At this stage, John Horgan would probably be asked to become Premier by the LtG.
Horgan would then need to submit his own Throne Speech.
This is where things get tricky. Clark says the then-current speaker will resign, and that no Liberal will run for Speaker. This means it is possible that an NDP MLA will need to become Speaker. This would mean 1 speaker, 43 Liberals, and 43 Coalition members. The Throne Speech would thus be a tie.
However, according to tradition, the speaker votes against VONC motions, and so, a throne speech may well pass. Clark could even have an MLA or two sit out the vote specifically so it does.
The problem comes when it is budget time, as there is simply no way the Coalition, under these circumstances, could pass a budget. The speaker would likely have to vote against it, and this would bring down the government.
It gets even more complicated.
While I can find information saying Denison's rules would have a speaker vote against both Budgets and Amendments to the Throne Speech; I can't find the rules for the speech itself; however, given amendments are given special attention as a "no" it would imply that yes, a speaker is to support a governments throne speech. Regardless, the sitting speaker may simply decide that Denison's rules are unclear, or, outdated, and vote against a Throne Speech, or vote for Budgets.
Additionally, the LtG could simply decide that Horgan can not actually obtain the confidence of the house, and, as a result, refuse his request to be Premier and simply call another election.
The Coalition's best hope is for a Liberal to agree to be speaker under an NDP Government. The reason this is unlikely is that the current speaker, Linda Reid, almost certainly was spoken to (by Clark) prior to her announcement, and, any Liberal agreeing to do this, would be ending their political career.
Finally; things could simply play out as Clark intends. She'd fail the VONC, Horgan would become Premier, lose his majority, win his VONC, but fail at his first budget. This could mean a year of NDP government without a majority in the Legislature. Why would Clark do this?
The simple answer is that governing is hard. The NDP will almost certainly not be able to carry out everything they planned to, even if they had a majority of their own. Additionally, there may be things she knows that we do not - for example, there may be a hidden deficit that will require unpopular cuts. Lastly, there were many Green voters who wanted the party to go into coalition with the Liberals. Clark can now say to all of them that the only way to get a Liberal government is to vote Liberal and that a vote for the Greens is a vote for the NDP.
In the end, this is a good strategy from Clark that has one major flaw; it requires loyalty. That does not mean I expect any BC Liberal MLA to join the NDP, or, agree to sit as speaker under an NDP government, but, MLAs get job offers from private firms from time to time, and in order for Clark to maintain the 43 seats she needs to block the Coalition, she will require each and every MLA to remain in the legislature and not decide to leave for a better job, or even for personal reasons. If as much as one BCL MLA resigns, this entire strategy unravels, and should the by-election result in a Coalition victory, it is game over for Christy Clark.