Nobody gives Parker warnings to the jury. No judge says to the jury "if you fail to appear, the trial will continue without you". If they did, then the jury might feel free to stay home instead of being afraid someone would come looking for them. So what do you do if parts of your jury don't show up when they're supposed to? CPL 270.35(2)(a) is one of the better statutes in terms of being specific. Basically, any juror who does not return within two hours can be replaced.
It's not quite that simple. Upon learning that one of our jurors is missing, the trial judge is required to conduct a "reasonably thorough inquiry" to determine whether the juror is reasonably likely to return within two hours of the time court was scheduled to resume. This is why the ADA will call the area hospitals. It's like advertising in the Daily Record to give notice to someone you know is living in . Pointless though they may be, the formalities must be observed.
As to the two hours, note that it's not two hours from the time of the phone call. If the juror will not return within two hours of the time set for the trial to continue, then the juror can be replaced. So if you find out about problems at 4PM today and the trial is supposed to continue tomorrow at noon, any juror due back by two tomorrow cannot be replaced. If you find out about the problem at 4PM, and court was scheduled to begin again at 2:30, any juror not due back until after 4:30 can be excused. You have a right to be heard before any juror is excused, and the court must place the reasons for dismissal on the record (CPL 270.35[b&c]).
What if the jury is deliberating? The judge cannot replace a deliberating juror without the defendant's express written consent, executed in open court (CPL 270.35; People v Gomez, 308 AD2d 460 [2d Dept 2003]). The defense doesn't need a good reason - or any reason - to refuse to consent. If you think replacing the deliberating juror would be a mistake, then the court must declare a mistrial and schedule a new trial date.