I understand that you want to know how MATLAB handles the Kernel density options for 'support' in the "fitdist" function. The documentation page of the function does not provide enough explanation of the Kernel density options for 'support'.
Similar options for 'support' exist in another function "ksdensity", which provides Kernel smoothing function estimate for univariate and bivariate data. The explanation provided for this function is listed as follows:
" *'Support' — Support for the density 'unbounded' (default) | 'positive' | two-element vector, [L U] | two-by-two matrix, [L1 L2 ; U1 U2] Support for the density, specified as the comma-separated pair consisting of 'support' and one of the following.
'unbounded' Default. Allow the density to extend over the whole real line. 'positive' Restrict the density to positive values. Two-element vector, [L U] Give the finite lower and upper bounds for the support of the density. This option is only valid for univariate sample data. Two-by-two matrix, [L1 L2 ; U1 U2] Give the finite lower and upper bounds for the support of the density. The first row contains the lower limits and the second row contains the upper limits. This option is only valid for bivariate sample data. For univariate data, if 'Support' is 'positive', then ksdensity transforms x using a log function, estimates the density of the transformed values, and transforms back to the original scale. If 'Support' is a vector [L U], then ksdensity uses the transformation log((X-L)/(U-X)). The Bandwidth parameter and bw outputs are on the scale of the transformed values.
For bivariate data, 'Support' can be a combination of positive, unbounded, or bounded variables specified as [0 -Inf ; Inf Inf] or [0 L ; Inf U]. ksdensity transforms each dimension of x in the same way as the univariate data. The 'Bandwidth' parameter and bw outputs are on the scale of the transformed values.*"
Please refer to the "Name-Value Pair Arguments" section in the following link: