Confused with filtering linear chirp signal using band-pass filter
You are seeing the difference between "wide band FM" and "narrow band FM" in your modulated waveform. Observe your modulation index for each case and then review the sideband levels versus mod index using Bessel functions. (The modulation index is the ratio of the frequency deviation over the frequency modulation). The first case is wide-band FM as your deviation (approximately +/-500 Hz) is significantly larger than your mod rate (50 Hz), so the mod index is >>1. The second case is narrow band FM as your deviation is significantly smaller than your mod rate (9850) and the mod index is &lt;&lt;1.  Narrow band FM will have only one pair of significant sidebands that will be at the mod rate offset from your carrier; while wideband FM will have a significant number of sidebands each spaced at your modulation rate and going out slightly beyond your deviation before becoming insignificant. 

So when you are doing narrow band FM with one pair of sidebands, note that your signal will be dominantly your carrier with two sidebands that are each 9850 Hz away! You are seeing leakage products at your filter output; notice how small the amplitude is compared to the first case.  (Given your modulation is a ramp and not a sine wave, you will actually have multiple sidebands for each of the Fourier series components of your ramp signal, but the point is these will all be spaced by 9850 Hz from your carrier frequency which will also be dominant given the small moduation index). 

While in your wideband case you will have spectral energy at spacing every 50 Hz with approximately 1KHz total bandwidth (review Carson's rule on this) and thus will provide tones that will pass through your filter.

Below is a plot of the Bessel function of the first kind from this site:
http://www.statsref.com/HTML/index.html?key_functions.html

This shows the relative level of the carrier (given by $J_0(x)$) and the first five sidebands $J_1(x), J_2(x),J_3(x),J_4(x), J_5(x) $ at a given modulation index x.