Classification - Modelling Irreversible Process I am interested in classification problems on time series (or any set of inputs where order must be preserved) where you have additional information about the target variable that once it changes class, it cannot change back i.e. modelling some irreversible process. Let me give an example below to illustrate:
Suppose you are classifying the presence of an irreversible condition in humans (e.g. arthritis present, arthritis not present - assuming that once arthritis has developed it is unfortunately permanent).
You are using a classification model on time series data (where you have data from across multiple people), and a number of input features e.g.

*

*Features/Inputs: X1 = Age, X2 = Cumulative Miles Ran, X3 = Family History Quantified

*Target Variable to be Modelled: Y = 1 if Arthritis Present and 0 If not

As the process of Arthritis is unfortunately irreversible, when the target variable changes from 0 to 1 (for a given person) it does not change back e.g. an example of your dataset for a given person might look like:
Time Person X1. X2     X3.    |  Y
2010   1    50  1000   0.7       0
2011   1    51  2000   0.7       0
2012   1    52  3000   0.7       0
... 
2018   1    58  20000  0.7       1
2019   1    59  22000  0.7       1
2020   1    60  24000  0.7       1

My question is:

*

*Do any techniques or methods exist for incorporating this additional information in your model? i.e. occurrence of the negative class cannot occur after the positive class

*My ideas would be: A) using a sequence model B) or feeding previous predictions in c) custom loss function to additionally penalise class changes - is there any literature on this?

 A: Your example is a data set with explanatory data matrix $X_{T \times 3}$ and target data vector $Y_{T \times 1}$.
If your understanding of the "true" dynamics of $Y$ is correct, the state can vary over time, from absent to present.  However, present is an absorbing state.
Target variable $Y_t$ could be modeled with an observation equation, a composite of true state $\theta_t$ and observation noise $\epsilon_t$, $Y_t = \theta_t + \epsilon_t$. This allows observations that appear to be nonsensical as observed. Observed states $y_t$ could be "flipped" from true state $\theta_t$ due to the observation noise $\epsilon_t$.
Alternatively, if you assert there is no observation error, some of the observations are "wrong", and you may choose to drop "wrong" observations from the data set in a data cleaning step before you start modeling.  The important point is that "data cleaning" does not impact the form of model you are constructing, but rather "data cleaning" would impact the training data you will use to build you model.
Once you begin modeling, it appears from the example context given that you have two monotonically increasing explanatory variables, age and miles run. The last explanatory variable appears static, family features.  If family history updates over time, this too would be at least partially monotonic, family arthritis absent==0 $\rightarrow$ present==1.
Assuming you use logistic regression to generate class probabilities $P(y_t=\mathsf{absent~} | X_t)$ and $P(y_t=\mathsf{present~} | X_t)$, if you place non-negativity constraints on the logistic regression coefficients, the output class probability in your model will be monotonic in time:
$$ 
P(y_t = \mathsf{present~} | X_t) \ge P(y_{t-1} = \mathsf{present~} | X_{t-1}) 
$$
In a Bayesian framework, you can use a prior for the regression coefficients which enforces non-negative results.  Alternatively, you could use non-negative least squares when fitting your logistic regression coefficients for the monotonic explanatory variables.
