Attached and detached are two states with two answers
Motor wordings generally treat a trailer as an extension of the towing vehicle while it is properly coupled, and as an unrelated object once it is not. That single distinction governs most of what follows. A trailer that rolls into a wall while hitched is normally within the liability the policy covers; the same trailer rolling into the same wall while parked on a driveway usually is not.
The reason is that motor liability attaches to the use of a vehicle on a road, and a detached trailer is not being used as part of any vehicle at that moment. Some wordings extend cover briefly during coupling and uncoupling. Many do not mention it at all.
Liability follows the towing vehicle while coupled
Where a trailer causes injury or damage to someone else while being towed, the towing vehicle’s liability cover is normally the section that responds, since the combination is treated as one unit under most legal regimes. This is the part of towing cover that tends to be automatic, and it is also the part the law in a given jurisdiction is most likely to compel.
It is worth noticing what that automatic cover is: liability only. It protects other people from the trailer. It does nothing at all for the trailer, and nothing for the load, which is exactly the misunderstanding that produces disappointment after a jack-knife on a wet slip road.
The trailer itself is property and property needs its own cover
A trailer, a horsebox or a plant carrier is a valuable object in its own right, and comprehensive cover on the towing vehicle does not usually extend to repairing or replacing it. Where such cover is offered it is typically an extension bought specifically, or a separate policy on the trailer, sometimes underwritten more like specialist property insurance than like motor insurance.
Theft is the sharper problem. Trailers are stolen because they are portable, hard to identify and easy to sell, and cover against that generally requires a dedicated policy with its own security conditions about hitch locks, wheel clamps and where the trailer is kept. Those conditions are enforced, and failing one can defeat the claim.
Weight and licence entitlement can quietly move the whole question
Every licensing regime sets limits on what a given category of licence permits a driver to tow, usually built from the weight of the towing vehicle, the weight of the trailer and the total of both. These thresholds are local, they have been revised in several countries in recent years, and they are not intuitive.
The insurance consequence is severe and indirect. Almost every motor policy excludes loss occurring while the vehicle is being driven otherwise than in accordance with the driver’s licence, so exceeding a towing entitlement can put an entire claim outside cover, including the liability section in some regimes. That is a licensing question first, and it must be checked against the rules where the vehicle is being driven.
Caravans, contents and the touring case
A touring caravan raises everything above plus a contents question, since a caravan carries possessions the way a home does rather than the way a boot does. Dedicated caravan policies exist precisely because the combination of a valuable shell, valuable contents and long periods parked in unfamiliar places is not something a motor wording is built to price.
Cross-border touring adds another layer, because both the towing cover and any separate trailer policy carry their own territorial limits, and they are not necessarily the same limits. Some jurisdictions also require trailers above a certain weight to be separately registered or separately insured, which is a rule to establish before departure rather than at a border.
Fitting a towbar is a declarable change
A towbar is an alteration to the vehicle as it left the factory, and most insurers expect to be told about one even though it rarely moves a price by much on its own. What moves the price is the use: regular towing changes the exposure, and a wording may treat frequent towing of heavy loads as commercial use depending on what is being moved and why.
None of this is uniform. Some policies include liability while towing without comment, some require the trailer to be declared, and a few exclude towing for reward entirely. The policy wording governs, market practice differs considerably, and the sensible order is to establish what the licence permits, then what the policy covers, then what the trailer itself needs.