What would be the effect of an abstention vote by four US senators on a question of whether to confirm a Supreme Court nominee, if the result were that there were only 49 votes in favor of confirming the nominee?
The answer to your question depends on the form of the abstention. The most important question to answer is: Are the abstaining Senators present for the vote?
If the abstaining Senators are present: the abstention has no effect whatsoever. The voting standard to invoke cloture on a nomination is simple majority. Thus as long as more Senators vote in favor than against on the issue of cloture and then in favor of the nomination than against, the nomination carries the Senate. In the case the vote is tied the Vice-President would get to cast the deciding vote, even if the vote count is like 1 for and 1 against with another 50 Senators present, the Vice President would be able to cast a deciding vote. The abstaining Senators, in accordance with Rule XII of the Senate, would have to indicate their reasons for not voting, but still may abstain. The only requirement is that a majority of Senators are present in the room as this constitutes quorum for the Senate to do business. Once quorum is attained, a majority of those voting is sufficient to carry cloture on a nomination and approving the nomination.
If the Senators abstain by not being present, the question is if there is enough Senators in the room to obtain quorum. If enough Senators are present in the Senate (currently, 51 Senators or more, this number drops to 50 if any one Senator dies or resigns and a replacement is not yet appointed) then this form of abstention also does not matter. The real deal is if a sufficient number of Senators abstain from the vote by not being present in the Senate. This would require 50 or more Senators to not be present. In that case, the Senate cannot conduct business and so the Senate must adjourn or adopt measures to force attendance of absent members (i.e. resolve for the Sergeant-at-Arms of the Senate to go ahead and arrest absent members and bring them to the Senate).
Thus to answer your question in full: generally there is no effect of abstaining from a vote. Thus in the exact situation you provided where four Senators abstain, the votes for the affirmative are counted. The votes for the negative are counted. If there is more affirmative votes than negative votes the nomination is approved. If there is an equal amount the Vice President can cast a deciding vote, but does not have to. In the case the vote remains tied, the nomination fails. If there are more negative votes the nomination fails.
What the minority Senate caucus could do if they persuade four Senators to abstain and not be present is all agree to leave the Senate. In that case the Senate would be left without quorum. Without quorum no action could be taken. However, if those Senators just abstain from the vote, but are present, a vote of 49-47 (for example) in favor of the nomination would be sufficient to confirm it.
Although this situation may sound unlikely it is theoretically possible: since the minority caucus consists of 49 Senators and if Senator McCain is ill and cannot attend the Senate, this leaves the majority with only 50 Senators. If the entire minority leaves and perhaps goes to Canada, outside the reach of US authorities, this could prevent the Senate from taking any action. In that case the Senate would have to adjourn until Senator McCain could come and provide quorum or until some sort of agreement is made to coax back absent Senators.
Furthermore, since each House of Congress is permitted to make its own procedures on how quorum is established it appears the minority caucus would need another confederate who wishes to assist them in securing the absence of quorum if they attempt to leave the Senate without quorum while the Senate is in session. This can be done by asking another member to suggest the absence of quorum while at least 50 Senators are absent or by leaving after the Senate is found to be without quorum (and having that member actually do that). According to the Senate rules on quorum, quorum is presumed. Yet it seems that Senate precedent requires the Chair to order a quorum call if a quorum of Senators did not vote on a particular issue, see here:
Where less than a quorum votes and the number of pairs announced are not sufficient to make a quorum, it is the duty of the chair to order a quorum call; the vote is valid if a quorum was present, even if a quorum did not vote, provided that a number of those not voting, sufficient to make a quorum, announced they were present but paired.
Thus if the chair follows precedent, the nomination does not occur, if the chair declines to, then a member would need to suggest an absence of quorum. If this is not done, then perhaps the Senate will approve a nominee because quorum has been "presumed".
It would be remiss to not also mention that according to rule VI.4 once quorum is lost it can only be reestablished through an affirmative quorum call:
...and until a quorum shall be present, no debate nor motion, except to adjourn, or to recess pursuant to a previous order entered by unanimous consent, shall be in order.
Thus if the Senate finds itself without quorum, say by asking for quorum in the early hours of the morning after a long Senate session, or at times when only a member of the minority and majority are present to pass routine matters, quorum can only be re-established by the presence of the majority of the Senators. This can be used to defeat the technical presence of quorum technique.