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Someone posted the following trivia on a social media website:

Do you know that pen caps have holes so that if someone swallows a cap, then air could still pass through?

This started a small debate, with some saying that the needed volume of air for respiration is too demanding and that the hole is too small, and others just approving of the assertion.

I made a quick search and found an article on iflscience, which is rather ironic about the issue, than it clears the things out. They cite a statement from the BIC's FAQ list that proves at least this didn't randomly start:

The reason that some BIC® pens have a hole in their cap is to prevent
the cap from completely obstructing the airway if accidently inhaled.
This is requested by the international safety standards ISO11540,
except for in cases where the cap is considered too large to be a
choking hazard.

I imagine choking on a pen cap has more consequences, but I am wondering whether this assertion is true and whether there is any science behind it.

The BIC FAQ says the hole in the cap is to prevent children from choking to death.

It was quoted in the question:

The reason that some BIC® pens have a hole in their cap is to prevent the cap from completely obstructing the airway if accidently inhaled. This is requested by the international safety standards ISO11540, except for in cases where the cap is considered too large to be a choking hazard.

That leads to an ISO standard which is specifically about preventing choking hazards in writing instruments used by children:

1. Scope

This International Standard specifies requirements to reduce the risk of asphyxiation from caps for writing and marking instruments. It relates to such instruments which in normal or foreseeable circumstances are likely to be used by children up to the age of 14 years.

So, I'd say it is pretty clear that the hole in pen caps is to prevent choking deaths, and that the social media trivia you read is correct.

The introduction of the international standard ISO 11540:2014 “Writing and marking instruments — Specification for caps to reduce the risk of asphyxiation” already makes clear that the intention of the design is to reduce the risk of asphyxiation for children.

If a child inhales a pen cap it might become lodged below the larynx and block the trachea. The risk of asphyxiation can be reduced if the pen cap is ventilated or too large to enter the airway. Children have to be actively discouraged from sucking, chewing, or putting pen caps in their mouths. A way of avoiding the risk of inhalation of caps of writing and marking instruments is to manufacture products without caps whenever possible. However, if caps are essential, the provisions of ISO 11540 minimize risk by specifying the design and performance of ventilated caps which reduce the likelihood of inhalation and delays asphyxiation pending medical intervention.

Strictly speaking, the scope is limited to children up to the age of 14 years.

This International Standard specifies requirements to reduce the risk of asphyxiation from caps for writing and marking instruments. It relates to such instruments which in normal or foreseeable circumstances are likely to be used by children up to the age of 14 years.

Nevertheless, this alone does not explain that this aspect of the design can be realized with a hole in the cap and that such a hole would be sufficient for this purpose.

This information, however, is given in Subsection 3.3 of the standard.

When tested in accordance with Annex A, caps shall permit a minimum air flow of 8 l/min, measured at room temperature, with a maximum pressure drop of 1,33 kPa.

NOTE 1 For caps relying on internal ventilation, a singular circular orifice with a cross-sectional area of approximately 3,4 mm² can be expected to satisfy this criterion, but multiple small orifices might require a larger total cross-sectional area.

(…)

NOTE 3 Caps conforming to this subclause are deemed to not present an asphyxiation hazard.

Remarkably, an air flow of 8 l/min or 0.48 m³/h corresponds to the reference respiratory value for a 15-year-old male sitting awake given in ICRP, (1994) “Human Respiratory Tract Model for Radiological Protection”. ICRP Publication 66. Ann. ICRP 24 (1–3). Therefore, the designed air flow rate may indeed be considered sufficient to reduce the risk of asphyxiation for children up to the age of 14 years.