Unsurroundable is a rare but valuable trait, one that counters harassment in melee combat.
← This is the icon it had before Dominions 6, which this wiki still uses on stat sheets.
Harassment simulates how units get distracted by having many foes fighting them at the same time. Each melee attack directed at them in a combat round reduces their Defence Skill by 1. Repel attempts done by the defender also increment the Harassment penalty, but failed attempts are not double-counted. Harassment cannot bring Defence Skill below zero, and harassment of mounts and their riders is counted separately.
There's an order to what parts of Defence Skill are reduced by Harrassment. First it takes your base Defence Skill. Then it takes the Parry bonus from your Shield; yes, Harrassment considers this Defence Skill. Then it takes the part of your Defence Skill granted by Armor and Shields; if your Defence Skill from these is negative, the penalty overlaps with Harrassment instead. Only once all of that is gone, does Harrassment go after the part of your Defence Skill granted by your Weapons.
The harassment penalty decays over periods where the subject is not attacked in melee, by a percentage. The per-round decay rate is not stated in the manual. In Dominions 5, the harassment penalty was multiplied by 95% every 16/375ths (somewhere between 1/23 and 1/24) of a combat round, so a full combat round without harassment reduced the penalty by just about 70%. The subject's Defense Skill modifiers return before their base Defense Skill, in reverse order of how they're listed; the Weapon Defense bonus comes back first (if the subject has one), followed by their Armor/Shield Defense bonus (if they have one, perhaps due to items), and then followed by the Parry bonus (if the subject has a Shield). Strangely, these bonuses appear to return even while being attacked, though that may just be the formula bugging out at such high values.
A point of Unsurroundable makes it so the first instance of harassment applied in a combat round doesn't count. Two points [i.e. Unsurroundable (2)] makes it so the first two instances that round are ignored, three points ignores three instances, and so on.
Generally, Unsurroundable is conferred by having additional pairs of eyes somewhere. For instance, the full-sized Hydras of Sauromatia and Pythium have Unsurroundable (4) because they have four extra heads, and this decreases by one point with each head they lose.