It sounds as if you are describing a procedure for modifying the separating hyperplane in a support vector machine (SVM).
The problem is that vector has two meanings in this context, and this is creating confusion in your sentence.
The input to an SVM of the type you are describing is a series of classified observations, where each observation is a point in an n-dimensional space, and the classifier is a binary 1 or 0. The observation point is described by its observation vector.
The hyperplane is described by a linear equation with n-1 coefficients. These coefficients are calculated so that the hyperplane separates the “0-classified” points from the “1-classified” points as much as possible.
The meaning of as much as possible is defined in terms of the support vectors, which are the normal vectors from the observation points to the hyperplane. Basically, “best” hyperplane coefficients are those which minimize the sum of the squared lengths of the normal vectors.
In the process you are describing, when a new observation point arrives, and is found to lie far from the existing hyperplane, this new point is added to the set of points used to compute the hyperplane coefficients, and new coefficients are calculated. This may be loosely referred to as “iteratively retraining the SVM”.
The support vector for the newly added point may be long, but it is not technically correct to say that this vector is far from the hyperplane, since it actually connects the hyperplane to the observation point.
Nor is it accurate to say that the observation vector is far from the hyperplane. The observation vector connects the origin point in the n-dimensional space with the observation point. It is not impossible for the hyperplane to include the origin, and also not impossible for the origin and the observation points to lie on opposite sides of the hyperplane.
Using the mathematical concepts more carefully, your description could be rephrased as follows:
Their approach allows for the retraining of the SVM after each new observation point. If a point is classified with high confidence (lying beyond a specified distance from the separating hyperplane), then the hyperplane coefficients are updated. This is appled only when the classification corresponds to a rejection.